[{"author":[{"last_name":"Hurm","first_name":"Christoph","full_name":"Hurm, Christoph"},{"first_name":"Maximilian","last_name":"Moser","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian"}],"day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"publication_identifier":{"issn":["0936-7195"],"eissn":["1522-2608"]},"project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"ddc":["510"],"external_id":{"arxiv":["2402.13790"]},"article_processing_charge":"Yes (via OA deal)","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"success":1,"file_size":513741,"checksum":"6bac9d3e566b68519ae80ac8b0f41f20","content_type":"application/pdf","relation":"main_file","date_updated":"2025-06-03T09:12:22Z","date_created":"2025-06-03T09:12:22Z","creator":"dernst","file_name":"2025_GAMM_Hurm.pdf","file_id":"19786","access_level":"open_access"}],"scopus_import":"1","publication":"GAMM-Mitteilungen","article_number":"e70003","OA_type":"hybrid","file_date_updated":"2025-06-03T09:12:22Z","year":"2025","publication_status":"published","intvolume":" 48","type":"journal_article","title":"Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model","citation":{"ieee":"C. Hurm and M. Moser, “Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model,” GAMM-Mitteilungen, vol. 48, no. 2. Wiley, 2025.","short":"C. Hurm, M. Moser, GAMM-Mitteilungen 48 (2025).","apa":"Hurm, C., & Moser, M. (2025). Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model. GAMM-Mitteilungen. Wiley. https://doi.org/10.1002/gamm.70003","mla":"Hurm, Christoph, and Maximilian Moser. “Nonlocal‐to‐local Convergence for a Cahn–Hilliard Tumor Growth Model.” GAMM-Mitteilungen, vol. 48, no. 2, e70003, Wiley, 2025, doi:10.1002/gamm.70003.","chicago":"Hurm, Christoph, and Maximilian Moser. “Nonlocal‐to‐local Convergence for a Cahn–Hilliard Tumor Growth Model.” GAMM-Mitteilungen. Wiley, 2025. https://doi.org/10.1002/gamm.70003.","ama":"Hurm C, Moser M. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model. GAMM-Mitteilungen. 2025;48(2). doi:10.1002/gamm.70003","ista":"Hurm C, Moser M. 2025. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model. GAMM-Mitteilungen. 48(2), e70003."},"OA_place":"publisher","arxiv":1,"abstract":[{"lang":"eng","text":"We consider a local Cahn–Hilliard‐type model for tumor growth as well as a nonlocal model where, compared to the local system, the Laplacian in the equation for the chemical potential is replaced by a nonlocal operator. The latter is defined as a convolution integral with suitable kernels parametrized by a small parameter. For sufficiently smooth bounded domains in three dimensions, we prove convergence of weak solutions of the nonlocal model toward strong solutions of the local model together with convergence rates with respect to the small parameter. The proof is done via a Gronwall‐type argument and a convergence result with rates for the nonlocal integral operator toward the Laplacian due to Abels and Hurm."}],"publisher":"Wiley","date_published":"2025-06-01T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","month":"06","issue":"2","acknowledgement":"C. Hurm was partially supported by the Graduiertenkolleg 2339 IntComSin of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–Project-ID 321821685. M. Moser has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 948819). The support is gratefully acknowledged. Finally, we thank Daniel Böhme and Jonas Stange for careful proofreading. Open Access funding enabled and organized by Projekt DEAL.","oa_version":"Published Version","article_type":"original","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.1002/gamm.70003","_id":"19783","status":"public","date_created":"2025-06-03T08:58:01Z","volume":48,"date_updated":"2025-06-03T09:14:17Z"},{"day":"01","author":[{"orcid":"0000-0002-9573-2962","last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"full_name":"Hieber, Matthias","first_name":"Matthias","last_name":"Hieber"},{"last_name":"Hussein","first_name":"Amru","full_name":"Hussein, Amru"},{"full_name":"Saal, Martin","last_name":"Saal","first_name":"Martin"}],"publication_identifier":{"issn":["1050-5164"]},"project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"ec_funded":1,"publication":"Annals of Applied Probability","scopus_import":"1","article_processing_charge":"No","external_id":{"arxiv":["2210.05973"],"isi":["001434322900016"]},"intvolume":" 35","publication_status":"published","year":"2025","OA_type":"green","citation":{"ama":"Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with nonisothermal turbulent pressure. Annals of Applied Probability. 2025;35(1):635-700. doi:10.1214/24-AAP2124","ista":"Agresti A, Hieber M, Hussein A, Saal M. 2025. The stochastic primitive equations with nonisothermal turbulent pressure. Annals of Applied Probability. 35(1), 635–700.","ieee":"A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with nonisothermal turbulent pressure,” Annals of Applied Probability, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 635–700, 2025.","apa":"Agresti, A., Hieber, M., Hussein, A., & Saal, M. (2025). The stochastic primitive equations with nonisothermal turbulent pressure. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-AAP2124","mla":"Agresti, Antonio, et al. “The Stochastic Primitive Equations with Nonisothermal Turbulent Pressure.” Annals of Applied Probability, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 635–700, doi:10.1214/24-AAP2124.","short":"A. Agresti, M. Hieber, A. Hussein, M. Saal, Annals of Applied Probability 35 (2025) 635–700.","chicago":"Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Nonisothermal Turbulent Pressure.” Annals of Applied Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/24-AAP2124."},"OA_place":"repository","arxiv":1,"type":"journal_article","title":"The stochastic primitive equations with nonisothermal turbulent pressure","department":[{"_id":"JuFi"}],"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.05973","open_access":"1"}],"date_published":"2025-02-01T00:00:00Z","abstract":[{"lang":"eng","text":"In this paper, we introduce and study the primitive equations with non-isothermal turbulent pressure and transport noise. They are derived from the Navier–Stokes equations by employing stochastic versions of the Boussinesq and the hydrostatic approximations. The temperature dependence of the turbulent pressure can be seen as a consequence of an additive noise acting on the small vertical dynamics. For such a model we prove global well-posedness in H^1 where the noise is considered in both the Itô and Stratonovich formulations. Compared to previous variants of the primitive equations, the one considered here presents a more intricate coupling between the velocity field and the temperature. The corresponding analysis is seriously more involved than in the deterministic setting. Finally, the continuous dependence on the initial data and the energy estimates proven here are new, even in the case of isothermal turbulent pressure."}],"publisher":"Institute of Mathematical Statistics","acknowledgement":"The first author thanks Umberto Pappalettera for helpful suggestions on Section 2 and for bringing to his attention the reference [56]. The first author is grateful to Marco Romito for helpful comments related to Remarks 2.1 and 2.2. Finally, the first author thanks Caterina Balzotti for her support in creating the picture.\r\nAntonio Agresti has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819). Antonio Agresti is a member of GNAMPA (INδAM).\r\nMatthias Hieber gratefully acknowledges the support by the Deutsche Forschungsgemeinschaft (DFG) through the Research Unit 5528—project number 500072446.\r\nAmru Hussein has been supported by Deutsche Forschungsgemeinschaft (DFG)—project\r\nnumber 508634462 and by MathApp—Mathematics Applied to Real-World Problems—part\r\nof the Research Initiative of the Federal State of Rhineland-Palatinate, Germany.\r\nMartin Saal has been supported by Deutsche Forschungsgemeinschaft (DFG)—project\r\nnumber 429483464.","oa_version":"Preprint","issue":"1","page":"635-700","month":"02","date_created":"2025-04-06T22:01:32Z","volume":35,"date_updated":"2025-09-30T11:23:58Z","doi":"10.1214/24-AAP2124","_id":"19505","isi":1,"status":"public","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"article_type":"original"},{"corr_author":"1","OA_type":"green","year":"2025","publication_status":"published","intvolume":" 130","external_id":{"arxiv":["2109.04233"]},"article_processing_charge":"No","scopus_import":"1","publication":"Journal of Differential Geometry","ec_funded":1,"project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"eissn":["1945-743X"],"issn":["0022-040X"]},"author":[{"last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian","full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Laux","first_name":"Tim","full_name":"Laux, Tim"}],"day":"01","keyword":["Mean curvature flow","gradient flows","varifolds","weak solutions","weak-strong uniqueness","calibrated geometry","gradient-flow calibrations"],"article_type":"original","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.4310/jdg/1747065796","_id":"10011","status":"public","date_created":"2021-09-13T12:17:10Z","volume":130,"date_updated":"2025-05-28T09:27:05Z","month":"05","page":"209-268","oa_version":"Preprint","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813. The content of this paper was developed and parts of it were written during a visit of the first author to the Hausdorff Center of Mathematics (HCM), University of Bonn. The hospitality and the support of HCM are gratefully acknowledged.","abstract":[{"text":"We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow-is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.","lang":"eng"}],"publisher":"International Press","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2109.04233"}],"date_published":"2025-05-01T00:00:00Z","department":[{"_id":"JuFi"}],"quality_controlled":"1","type":"journal_article","title":"A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness","citation":{"ieee":"S. Hensel and T. Laux, “A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,” Journal of Differential Geometry, vol. 130. International Press, pp. 209–268, 2025.","mla":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.” Journal of Differential Geometry, vol. 130, International Press, 2025, pp. 209–68, doi:10.4310/jdg/1747065796.","apa":"Hensel, S., & Laux, T. (2025). A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. International Press. https://doi.org/10.4310/jdg/1747065796","short":"S. Hensel, T. Laux, Journal of Differential Geometry 130 (2025) 209–268.","chicago":"Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.” Journal of Differential Geometry. International Press, 2025. https://doi.org/10.4310/jdg/1747065796.","ama":"Hensel S, Laux T. A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. 2025;130:209-268. doi:10.4310/jdg/1747065796","ista":"Hensel S, Laux T. 2025. A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal of Differential Geometry. 130, 209–268."},"OA_place":"repository","arxiv":1},{"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ddc":["510"],"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"author":[{"last_name":"Abels","first_name":"Helmut","full_name":"Abels, Helmut"},{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X","first_name":"Julian L"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian","first_name":"Maximilian","last_name":"Moser"}],"day":"03","pmid":1,"article_number":"77","file_date_updated":"2024-09-09T08:43:32Z","year":"2024","publication_status":"published","intvolume":" 248","external_id":{"pmid":["39239088"],"arxiv":["2311.02997"],"isi":["001305530600001"]},"article_processing_charge":"Yes (via OA deal)","file":[{"success":1,"file_size":811131,"checksum":"98493a05b84e4513b6394dfad4851ddf","content_type":"application/pdf","relation":"main_file","date_updated":"2024-09-09T08:43:32Z","date_created":"2024-09-09T08:43:32Z","file_name":"2024_ArchiveRatAnalysis_Abels.pdf","creator":"dernst","file_id":"17938","access_level":"open_access"}],"scopus_import":"1","publication":"Archive for Rational Mechanics and Analysis","publisher":"Springer Nature","abstract":[{"text":"We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility mε>0 in the Allen-Cahn equation tends to zero in a subcritical way, i.e., mε=m0εβ for some β∈(0,2) and m0>0 . The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term mεHΓt in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow.","lang":"eng"}],"has_accepted_license":"1","date_published":"2024-09-03T00:00:00Z","quality_controlled":"1","department":[{"_id":"JuFi"}],"title":"Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system","type":"journal_article","arxiv":1,"citation":{"ista":"Abels H, Fischer JL, Moser M. 2024. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive for Rational Mechanics and Analysis. 248(5), 77.","ama":"Abels H, Fischer JL, Moser M. Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive for Rational Mechanics and Analysis. 2024;248(5). doi:10.1007/s00205-024-02020-9","chicago":"Abels, Helmut, Julian L Fischer, and Maximilian Moser. “Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” Archive for Rational Mechanics and Analysis. Springer Nature, 2024. https://doi.org/10.1007/s00205-024-02020-9.","apa":"Abels, H., Fischer, J. L., & Moser, M. (2024). Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-024-02020-9","ieee":"H. Abels, J. L. Fischer, and M. Moser, “Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system,” Archive for Rational Mechanics and Analysis, vol. 248, no. 5. Springer Nature, 2024.","mla":"Abels, Helmut, et al. “Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” Archive for Rational Mechanics and Analysis, vol. 248, no. 5, 77, Springer Nature, 2024, doi:10.1007/s00205-024-02020-9.","short":"H. Abels, J.L. Fischer, M. Moser, Archive for Rational Mechanics and Analysis 248 (2024)."},"article_type":"original","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"isi":1,"status":"public","doi":"10.1007/s00205-024-02020-9","_id":"17887","date_updated":"2025-09-08T09:11:41Z","volume":248,"date_created":"2024-09-08T22:01:10Z","month":"09","issue":"5","acknowledgement":"J. Fischer and M. Moser have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819).\r\nOpen Access funding enabled and organized by Projekt DEAL.","oa_version":"Published Version"},{"author":[{"last_name":"Agresti","orcid":"0000-0002-9573-2962","first_name":"Antonio","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}],"day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"ddc":["510"],"external_id":{"arxiv":["2206.00230"],"isi":["001154226500001"]},"article_processing_charge":"Yes (in subscription journal)","file":[{"date_created":"2024-07-22T09:21:09Z","date_updated":"2024-07-22T09:21:09Z","creator":"dernst","file_name":"2024_ProbTheory_Agresti.pdf","file_id":"17296","access_level":"open_access","file_size":942801,"success":1,"checksum":"b8572339dbc5b8de4934dc5fd34afc7d","content_type":"application/pdf","relation":"main_file"}],"scopus_import":"1","publication":"Probability Theory and Related Fields","file_date_updated":"2024-07-22T09:21:09Z","publication_status":"published","year":"2024","intvolume":" 188","type":"journal_article","title":"The critical variational setting for stochastic evolution equations","citation":{"ama":"Agresti A, Veraar M. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. 2024;188:957-1015. doi:10.1007/s00440-023-01249-x","ista":"Agresti A, Veraar M. 2024. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. 188, 957–1015.","mla":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” Probability Theory and Related Fields, vol. 188, Springer Nature, 2024, pp. 957–1015, doi:10.1007/s00440-023-01249-x.","ieee":"A. Agresti and M. Veraar, “The critical variational setting for stochastic evolution equations,” Probability Theory and Related Fields, vol. 188. Springer Nature, pp. 957–1015, 2024.","short":"A. Agresti, M. Veraar, Probability Theory and Related Fields 188 (2024) 957–1015.","apa":"Agresti, A., & Veraar, M. (2024). The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01249-x","chicago":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01249-x."},"arxiv":1,"abstract":[{"lang":"eng","text":"In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. Moreover, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equations, tamed Navier-Stokes equations, and Allen-Cahn equation."}],"publisher":"Springer Nature","date_published":"2024-04-01T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","month":"04","page":"957-1015","acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819) . The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","oa_version":"Published Version","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00440-023-01249-x","_id":"12485","isi":1,"status":"public","date_created":"2023-02-02T10:45:15Z","volume":188,"date_updated":"2025-09-04T11:27:46Z"},{"type":"journal_article","title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations","citation":{"ama":"Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. 2024;12:1907-1981. doi:10.1007/s40072-023-00319-4","ista":"Agresti A. 2024. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. 12, 1907–1981.","ieee":"A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 12. Springer Nature, pp. 1907–1981, 2024.","mla":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 12, Springer Nature, 2024, pp. 1907–81, doi:10.1007/s40072-023-00319-4.","apa":"Agresti, A. (2024). Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-023-00319-4","short":"A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024) 1907–1981.","chicago":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2024. https://doi.org/10.1007/s40072-023-00319-4."},"OA_place":"publisher","arxiv":1,"abstract":[{"text":"This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas.","lang":"eng"}],"publisher":"Springer Nature","date_published":"2024-09-01T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","month":"09","page":"1907-1981","oa_version":"Published Version","acknowledgement":"The author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti for her support in creating the picture. The author\r\nthanks the anonymous referee for helpful comments. ","article_type":"original","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.1007/s40072-023-00319-4","_id":"12486","status":"public","isi":1,"date_created":"2023-02-02T10:45:47Z","volume":12,"date_updated":"2025-08-05T13:23:09Z","author":[{"full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","orcid":"0000-0002-9573-2962","first_name":"Antonio"}],"pmid":1,"day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"project":[{"grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]},"ddc":["510"],"article_processing_charge":"No","external_id":{"arxiv":["2207.08293"],"isi":["001108594600001"],"pmid":["39104877"]},"file":[{"relation":"main_file","content_type":"application/pdf","checksum":"3c93d07a5f7e0b0caa8062eadcfa69c2","success":1,"file_size":1320682,"access_level":"open_access","file_id":"18787","file_name":"2024_StochPartDiffEquations_Agresti.pdf","creator":"dernst","date_updated":"2025-01-09T08:01:02Z","date_created":"2025-01-09T08:01:02Z"}],"scopus_import":"1","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","corr_author":"1","OA_type":"hybrid","file_date_updated":"2025-01-09T08:01:02Z","year":"2024","publication_status":"published","intvolume":" 12"},{"citation":{"ama":"Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 2024;190:485-541. doi:10.1007/s00440-023-01254-0","ista":"Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 190, 485–541.","apa":"Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0","ieee":"N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” Probability Theory and Related Fields, vol. 190. Springer Nature, pp. 485–541, 2024.","short":"N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024) 485–541.","mla":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields, vol. 190, Springer Nature, 2024, pp. 485–541, doi:10.1007/s00440-023-01254-0.","chicago":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0."},"OA_place":"publisher","arxiv":1,"type":"journal_article","title":"Annealed quantitative estimates for the quadratic 2D-discrete random matching problem","date_published":"2024-10-01T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","abstract":[{"text":"We study a random matching problem on closed compact 2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures μn and νm is quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure.","lang":"eng"}],"publisher":"Springer Nature","acknowledgement":"NC has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences.","oa_version":"Published Version","month":"10","page":"485-541","doi":"10.1007/s00440-023-01254-0","_id":"14797","status":"public","isi":1,"date_created":"2024-01-14T23:00:57Z","volume":190,"date_updated":"2025-09-04T11:43:43Z","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"language":[{"iso":"eng"}],"author":[{"first_name":"Nicolas","last_name":"Clozeau","full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b"},{"full_name":"Mattesini, Francesco","first_name":"Francesco","last_name":"Mattesini"}],"day":"01","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"project":[{"name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819"}],"ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"scopus_import":"1","publication":"Probability Theory and Related Fields","external_id":{"isi":["001136206200002"],"arxiv":["2303.00353"]},"article_processing_charge":"Yes (in subscription journal)","file":[{"file_id":"18788","access_level":"open_access","date_created":"2025-01-09T08:10:54Z","date_updated":"2025-01-09T08:10:54Z","file_name":"2024_ProbTheoryRelatFields_Clozeau.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":880117,"success":1,"checksum":"34f44cad6a210ff66791ee37e590af2c"}],"publication_status":"published","year":"2024","intvolume":" 190","corr_author":"1","OA_type":"hybrid","file_date_updated":"2025-01-09T08:10:54Z"},{"file_date_updated":"2025-01-09T08:23:36Z","OA_type":"hybrid","intvolume":" 390","publication_status":"published","year":"2024","file":[{"access_level":"open_access","file_id":"18790","creator":"dernst","file_name":"2024_MathAnnalen_Agresti.pdf","date_updated":"2025-01-09T08:23:36Z","date_created":"2025-01-09T08:23:36Z","relation":"main_file","content_type":"application/pdf","checksum":"d55cac8bddea09a97f06612825c4f229","success":1,"file_size":661557}],"external_id":{"isi":["001172711400002"],"arxiv":["2306.11081"],"pmid":["39351582"]},"article_processing_charge":"Yes (via OA deal)","publication":"Mathematische Annalen","scopus_import":"1","ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ddc":["510"],"project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"pmid":1,"day":"01","author":[{"full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","orcid":"0000-0002-9573-2962","first_name":"Antonio"},{"full_name":"Luongo, Eliseo","first_name":"Eliseo","last_name":"Luongo"}],"language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"article_type":"original","date_updated":"2025-09-04T12:19:59Z","volume":390,"date_created":"2024-03-10T23:00:54Z","isi":1,"status":"public","doi":"10.1007/s00208-024-02812-0","_id":"15098","page":"2727-2766","month":"10","acknowledgement":"The authors thank Professor Franco Flandoli for useful discussions and valuable insight into the subject. In particular, A.A. would like to thank professor Franco Flandoli for hosting and financially contributing to his research visit at Scuola Normale di Pisa in January 2023, where this work started. E.L. would like to express sincere gratitude to Professor Marco Fuhrman for igniting his interest in this particular field of research. E.L. want to thank Professor Matthias Hieber and Dr. Martin Saal for useful discussions. Finally, the authors thank the anonymous referee for helpful comments which improved the paper from its initial version.Open access funding provided by Scuola Normale Superiore within the CRUI-CARE Agreement. A. Agresti has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 948819).","oa_version":"Published Version","publisher":"Springer Nature","abstract":[{"text":"The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier–Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be interpreted as the physical law describing the driving mechanism on the atmosphere–ocean interface, i.e. as a balance of the shear stress of the ocean and the horizontal wind force.","lang":"eng"}],"quality_controlled":"1","department":[{"_id":"JuFi"}],"has_accepted_license":"1","date_published":"2024-10-01T00:00:00Z","title":"Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions","type":"journal_article","arxiv":1,"citation":{"ieee":"A. Agresti and E. Luongo, “Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions,” Mathematische Annalen, vol. 390. Springer Nature, pp. 2727–2766, 2024.","short":"A. Agresti, E. Luongo, Mathematische Annalen 390 (2024) 2727–2766.","apa":"Agresti, A., & Luongo, E. (2024). Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-024-02812-0","mla":"Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” Mathematische Annalen, vol. 390, Springer Nature, 2024, pp. 2727–66, doi:10.1007/s00208-024-02812-0.","chicago":"Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” Mathematische Annalen. Springer Nature, 2024. https://doi.org/10.1007/s00208-024-02812-0.","ama":"Agresti A, Luongo E. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. 2024;390:2727-2766. doi:10.1007/s00208-024-02812-0","ista":"Agresti A, Luongo E. 2024. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische Annalen. 390, 2727–2766."},"OA_place":"publisher"},{"article_number":"94","file_date_updated":"2024-04-23T07:30:48Z","year":"2024","publication_status":"published","intvolume":" 63","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001199418100002"],"arxiv":["2304.12096"]},"file":[{"date_updated":"2024-04-23T07:30:48Z","date_created":"2024-04-23T07:30:48Z","creator":"dernst","file_name":"2024_CalculusEquations_Abels.pdf","file_id":"15343","access_level":"open_access","success":1,"file_size":975186,"checksum":"b1095fad4cae596f52cc616a973bdde2","content_type":"application/pdf","relation":"main_file"}],"scopus_import":"1","publication":"Calculus of Variations and Partial Differential Equations","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"ddc":["510"],"author":[{"last_name":"Abels","first_name":"Helmut","full_name":"Abels, Helmut"},{"first_name":"Mingwen","last_name":"Fei","full_name":"Fei, Mingwen"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian","first_name":"Maximilian","last_name":"Moser"}],"day":"01","article_type":"original","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"language":[{"iso":"eng"}],"_id":"15334","doi":"10.1007/s00526-024-02715-7","status":"public","isi":1,"date_created":"2024-04-21T22:00:52Z","volume":63,"date_updated":"2025-09-04T13:45:40Z","month":"05","issue":"4","oa_version":"Published Version","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL.\r\nM. Fei was partially supported by NSF of China under Grant No. 12271004 and Anhui Provincial Funding Project under Grant Nos. gxbjZD2022009 and 2308085J10. Moreover, M. Moser has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 948819).","abstract":[{"text":"We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of vanishing mobility mε=ε√, where the small parameter ε>0 related to the thickness of the diffuse interface is sent to zero. For well-prepared initial data and sufficiently small times, we rigorously prove convergence to the classical two-phase Navier-Stokes system with surface tension. The idea of the proof is to use asymptotic expansions to construct an approximate solution and to estimate the difference of the exact and approximate solutions with a spectral estimate for the (at the approximate solution) linearized Allen-Cahn operator. In the calculations we use a fractional order ansatz and new ansatz terms in higher orders leading to a suitable ε-scaled and coupled model problem. Moreover, we apply the novel idea of introducing ε-dependent coordinates.","lang":"eng"}],"publisher":"Springer Nature","date_published":"2024-05-01T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","type":"journal_article","title":"Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility","citation":{"short":"H. Abels, M. Fei, M. Moser, Calculus of Variations and Partial Differential Equations 63 (2024).","mla":"Abels, Helmut, et al. “Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System in the Case of a Vanishing Mobility.” Calculus of Variations and Partial Differential Equations, vol. 63, no. 4, 94, Springer Nature, 2024, doi:10.1007/s00526-024-02715-7.","ieee":"H. Abels, M. Fei, and M. Moser, “Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility,” Calculus of Variations and Partial Differential Equations, vol. 63, no. 4. Springer Nature, 2024.","apa":"Abels, H., Fei, M., & Moser, M. (2024). Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-024-02715-7","chicago":"Abels, Helmut, Mingwen Fei, and Maximilian Moser. “Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System in the Case of a Vanishing Mobility.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2024. https://doi.org/10.1007/s00526-024-02715-7.","ama":"Abels H, Fei M, Moser M. Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility. Calculus of Variations and Partial Differential Equations. 2024;63(4). doi:10.1007/s00526-024-02715-7","ista":"Abels H, Fei M, Moser M. 2024. Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility. Calculus of Variations and Partial Differential Equations. 63(4), 94."},"arxiv":1},{"author":[{"full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962","last_name":"Agresti","first_name":"Antonio"},{"full_name":"Veraar, Mark","first_name":"Mark","last_name":"Veraar"}],"day":"01","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"ec_funded":1,"scopus_import":"1","publication":"SIAM Journal on Mathematical Analysis","article_processing_charge":"No","external_id":{"arxiv":["2301.06897"],"isi":["001315424500021"]},"year":"2024","publication_status":"published","intvolume":" 56","corr_author":"1","citation":{"ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems. SIAM Journal on Mathematical Analysis. 2024;56(4):4870-4927. doi:10.1137/23M1562482","ista":"Agresti A, Veraar M. 2024. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems. SIAM Journal on Mathematical Analysis. 56(4), 4870–4927.","short":"A. Agresti, M. Veraar, SIAM Journal on Mathematical Analysis 56 (2024) 4870–4927.","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems,” SIAM Journal on Mathematical Analysis, vol. 56, no. 4. Society for Industrial and Applied Mathematics, pp. 4870–4927, 2024.","mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative Systems.” SIAM Journal on Mathematical Analysis, vol. 56, no. 4, Society for Industrial and Applied Mathematics, 2024, pp. 4870–927, doi:10.1137/23M1562482.","apa":"Agresti, A., & Veraar, M. (2024). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1562482","chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative Systems.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1562482."},"arxiv":1,"type":"journal_article","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems","date_published":"2024-08-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.06897","open_access":"1"}],"department":[{"_id":"JuFi"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the d-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g. the Allen-Cahn equation), and dissipative systems (e.g. equations in coagulation dynamics). Moreover, we prove global well-posedness for two weakly dissipative systems: Lotka-Volterra equations for d∈{1,2,3,4} and the Brusselator for d∈{1,2,3}. Many of the results are also new without transport noise. The proofs are based on maximal regularity techniques, positivity results, and sharp blow-up criteria developed in our recent works, combined with energy estimates based on Itô's formula and stochastic Gronwall inequalities. Key novelties include the introduction of new Lζ -coercivity/dissipativity conditions and the development of an Lp(Lq) -framework for systems of reaction-diffusion equations, which are needed when treating dimensions d∈{2,3} in the case of cubic or higher order nonlinearities."}],"publisher":"Society for Industrial and Applied Mathematics","issue":"4","acknowledgement":"The first author’s research was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant 948819. . The second author’s research was supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","oa_version":"Preprint","month":"08","page":"4870-4927","doi":"10.1137/23M1562482","_id":"17372","isi":1,"status":"public","date_created":"2024-08-04T22:01:21Z","date_updated":"2025-09-08T08:46:57Z","volume":56,"article_type":"original","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}]},{"external_id":{"isi":["001285416500001"],"arxiv":["2309.06798"]},"article_processing_charge":"No","publication":"Multiscale Modeling and Simulation","scopus_import":"1","OA_type":"green","corr_author":"1","intvolume":" 22","publication_status":"published","year":"2024","day":"01","author":[{"full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b","first_name":"Nicolas","last_name":"Clozeau"},{"full_name":"Wang, Lihan","last_name":"Wang","first_name":"Lihan"}],"ec_funded":1,"project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"publication_identifier":{"issn":["1540-3459"],"eissn":["1540-3467"]},"page":"973-1029","month":"09","oa_version":"Preprint","acknowledgement":"We would like to thank our affiliations, Institute of Science and Technology Austria and Max Planck Institute for Mathematics in the Sciences, for supporting the authors’ visits to each other, which greatly facilitated this work. We would like to thank Marc Josien and Quinn Winters for assistance in numerical implementation.","issue":"3","language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"article_type":"original","date_updated":"2025-09-08T09:01:00Z","volume":22,"date_created":"2024-08-25T22:01:08Z","isi":1,"status":"public","doi":"10.1137/23M1603819","_id":"17462","title":"Artificial boundary conditions for random elliptic systems with correlated coefficient field","type":"journal_article","arxiv":1,"citation":{"short":"N. Clozeau, L. Wang, Multiscale Modeling and Simulation 22 (2024) 973–1029.","mla":"Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random Elliptic Systems with Correlated Coefficient Field.” Multiscale Modeling and Simulation, vol. 22, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 973–1029, doi:10.1137/23M1603819.","apa":"Clozeau, N., & Wang, L. (2024). Artificial boundary conditions for random elliptic systems with correlated coefficient field. Multiscale Modeling and Simulation. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1603819","ieee":"N. Clozeau and L. Wang, “Artificial boundary conditions for random elliptic systems with correlated coefficient field,” Multiscale Modeling and Simulation, vol. 22, no. 3. Society for Industrial and Applied Mathematics, pp. 973–1029, 2024.","chicago":"Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random Elliptic Systems with Correlated Coefficient Field.” Multiscale Modeling and Simulation. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1603819.","ama":"Clozeau N, Wang L. Artificial boundary conditions for random elliptic systems with correlated coefficient field. Multiscale Modeling and Simulation. 2024;22(3):973-1029. doi:10.1137/23M1603819","ista":"Clozeau N, Wang L. 2024. Artificial boundary conditions for random elliptic systems with correlated coefficient field. Multiscale Modeling and Simulation. 22(3), 973–1029."},"OA_place":"repository","publisher":"Society for Industrial and Applied Mathematics","abstract":[{"text":"We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale l in an infinite heterogeneous correlated random medium, in a situation where the medium is only known in a box of diameter L >>l around the support of the charge. We show that the algorithm in [J. Lu, F. Otto, and L. Wang, Optimal Artificial Boundary Conditions Based on Second-Order Correctors for Three Dimensional Random Ellilptic Media, preprint, arXiv:2109.01616, 2021], suggesting optimal Dirichlet boundary conditions motivated by the multipole expansion [P. Bella, A. Giunti, and F. Otto, Comm. Partial Differential Equations, 45 (2020), pp. 561–640], still performs well in correlated media. With overwhelming probability, we obtain a convergence rate in terms of l, L, and the size of the correlations for which optimality is supported with numerical simulations. These estimates are provided for ensembles which satisfy a multiscale logarithmic Sobolev inequality, where our main tool is an extension of the semigroup estimates in [N. Clozeau, Stoch. Partial Differ. Equ. Anal. Comput., 11 (2023), pp. 1254–1378]. As part of our strategy, we construct sublinear second-order correctors in this correlated setting, which is of independent interest.","lang":"eng"}],"quality_controlled":"1","department":[{"_id":"JuFi"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.06798"}],"date_published":"2024-09-01T00:00:00Z"},{"author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L","first_name":"Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer"},{"full_name":"Marveggio, Alice","id":"25647992-AA84-11E9-9D75-8427E6697425","last_name":"Marveggio","first_name":"Alice"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"14597"}]},"day":"24","ddc":["510"],"project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"publication_identifier":{"eissn":["1873-1430"],"issn":["0294-1449"]},"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","publication":"Annales de l'Institut Henri Poincare C","article_processing_charge":"Yes","external_id":{"isi":["001293853900003"]},"file":[{"relation":"main_file","content_type":"application/pdf","checksum":"b5ad02d9abd5b4701269cd1ad0a1cc8f","file_size":1348896,"success":1,"access_level":"open_access","file_id":"17923","creator":"dernst","file_name":"2024_AnnInstHPoincare_Fischer.pdf","date_created":"2024-09-09T07:46:42Z","date_updated":"2024-09-09T07:46:42Z"}],"publication_status":"published","year":"2024","intvolume":" 41","corr_author":"1","file_date_updated":"2024-09-09T07:46:42Z","citation":{"ista":"Fischer JL, Marveggio A. 2024. Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow. Annales de l’Institut Henri Poincare C. 41(5), 1117–1178.","ama":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow. Annales de l’Institut Henri Poincare C. 2024;41(5):1117-1178. doi:10.4171/AIHPC/109","chicago":"Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen–Cahn Equation towards Multiphase Mean Curvature Flow.” Annales de l’Institut Henri Poincare C. EMS Press, 2024. https://doi.org/10.4171/AIHPC/109.","apa":"Fischer, J. L., & Marveggio, A. (2024). Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow. Annales de l’Institut Henri Poincare C. EMS Press. https://doi.org/10.4171/AIHPC/109","ieee":"J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow,” Annales de l’Institut Henri Poincare C, vol. 41, no. 5. EMS Press, pp. 1117–1178, 2024.","mla":"Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen–Cahn Equation towards Multiphase Mean Curvature Flow.” Annales de l’Institut Henri Poincare C, vol. 41, no. 5, EMS Press, 2024, pp. 1117–78, doi:10.4171/AIHPC/109.","short":"J.L. Fischer, A. Marveggio, Annales de l’Institut Henri Poincare C 41 (2024) 1117–1178."},"title":"Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow","type":"journal_article","has_accepted_license":"1","date_published":"2024-01-24T00:00:00Z","quality_controlled":"1","department":[{"_id":"JuFi"}],"publisher":"EMS Press","abstract":[{"text":"Phase-field models such as the Allen–Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen–Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow. In the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: as long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen–Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε \r\n1/2\r\n ). Our approach is based on the gradient-flow structure of the Allen–Cahn equation and its limiting motion: building on the recent concept of “gradient-flow calibrations” for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen–Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen–Cahn operator or additional convergence hypotheses for the energy at positive times.","lang":"eng"}],"issue":"5","acknowledgement":"The authors thank Sebastian Hensel for useful and helpful commentson the first draft of this work.\r\nThis project has received funding from the European Research Council (ERC)\r\nunder the European Union’s Horizon 2020 research and innovation programme (grant\r\nagreement no. 948819.","oa_version":"Published Version","month":"01","page":"1117-1178","isi":1,"status":"public","_id":"17481","doi":"10.4171/AIHPC/109","date_updated":"2025-09-08T09:11:01Z","volume":41,"date_created":"2024-09-01T22:01:09Z","article_type":"original","language":[{"iso":"eng"}],"oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"doi":"10.4171/IFB/484","_id":"13043","isi":1,"status":"public","date_created":"2023-05-21T22:01:06Z","volume":25,"date_updated":"2025-04-14T09:35:57Z","article_type":"original","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"issue":"1","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","oa_version":"Published Version","month":"04","page":"37-107","date_published":"2023-04-20T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","abstract":[{"text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction\r\nof a gradient flow calibration in the sense of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting along triple junctions.","lang":"eng"}],"publisher":"EMS Press","citation":{"short":"S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107.","apa":"Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1, EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484.","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS Press, pp. 37–107, 2023.","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023. https://doi.org/10.4171/IFB/484.","ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484","ista":"Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107."},"arxiv":1,"type":"journal_article","title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","year":"2023","publication_status":"published","intvolume":" 25","corr_author":"1","file_date_updated":"2023-05-22T07:24:13Z","scopus_import":"1","publication":"Interfaces and Free Boundaries","external_id":{"isi":["000975817300002"],"arxiv":["2108.01733"]},"article_processing_charge":"No","file":[{"checksum":"622422484810441e48f613e968c7e7a4","success":1,"file_size":867876,"relation":"main_file","content_type":"application/pdf","file_name":"2023_Interfaces_Hensel.pdf","creator":"dernst","date_updated":"2023-05-22T07:24:13Z","date_created":"2023-05-22T07:24:13Z","access_level":"open_access","file_id":"13045"}],"publication_identifier":{"eissn":["1463-9971"],"issn":["1463-9963"]},"project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"author":[{"last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"}],"day":"20","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10013"}]}},{"abstract":[{"text":"In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.","lang":"eng"}],"publisher":"Elsevier","department":[{"_id":"JuFi"}],"quality_controlled":"1","date_published":"2023-09-25T00:00:00Z","has_accepted_license":"1","type":"journal_article","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity","citation":{"apa":"Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity,” Journal of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.","short":"A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.","mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp. 247–300, doi:10.1016/j.jde.2023.05.038.","chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.","ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038","ista":"Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 368(9), 247–300."},"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"article_type":"original","date_created":"2023-06-18T22:00:45Z","volume":368,"date_updated":"2025-04-14T07:53:59Z","doi":"10.1016/j.jde.2023.05.038","_id":"13135","isi":1,"status":"public","page":"247-300","month":"09","acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 948819) Image 1. The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","oa_version":"Published Version","issue":"9","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"publication_identifier":{"eissn":["1090-2732"],"issn":["0022-0396"]},"project":[{"grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials"}],"ddc":["510"],"day":"25","author":[{"last_name":"Agresti","orcid":"0000-0002-9573-2962","first_name":"Antonio","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"first_name":"Mark","last_name":"Veraar","full_name":"Veraar, Mark"}],"file_date_updated":"2024-01-29T11:03:09Z","corr_author":"1","intvolume":" 368","publication_status":"published","year":"2023","file":[{"file_id":"14895","access_level":"open_access","date_updated":"2024-01-29T11:03:09Z","date_created":"2024-01-29T11:03:09Z","file_name":"2023_JourDifferentialEquations_Agresti.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","success":1,"file_size":834638,"checksum":"246b703b091dfe047bfc79abf0891a63"}],"external_id":{"isi":["001019018700001"]},"article_processing_charge":"Yes (in subscription journal)","publication":"Journal of Differential Equations","scopus_import":"1"},{"related_material":{"record":[{"relation":"part_of_dissertation","id":"11842","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"14597"}]},"day":"21","author":[{"id":"25647992-AA84-11E9-9D75-8427E6697425","full_name":"Marveggio, Alice","first_name":"Alice","last_name":"Marveggio"}],"project":[{"grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"issn":["2663-337X"]},"ddc":["515"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png"},"ec_funded":1,"file":[{"relation":"main_file","content_type":"application/pdf","checksum":"6c7db4cc86da6cdc79f7f358dc7755d4","success":1,"file_size":2881100,"access_level":"open_access","file_id":"14626","creator":"amarvegg","file_name":"thesis_Marveggio.pdf","date_updated":"2023-11-29T09:09:31Z","date_created":"2023-11-29T09:09:31Z"},{"relation":"source_file","content_type":"application/zip","checksum":"52f28bdf95ec82cff39f3685f9c48e7d","file_size":10189696,"access_level":"closed","file_id":"14627","creator":"amarvegg","file_name":"Thesis_Marveggio.zip","date_updated":"2024-03-20T12:28:32Z","date_created":"2023-11-29T09:10:19Z"}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","article_processing_charge":"No","year":"2023","supervisor":[{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X"}],"publication_status":"published","file_date_updated":"2024-03-20T12:28:32Z","corr_author":"1","OA_place":"publisher","citation":{"ama":"Marveggio A. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587","ista":"Marveggio A. 2023. Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria.","mla":"Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587.","ieee":"A. Marveggio, “Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences,” Institute of Science and Technology Austria, 2023.","short":"A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science and Technology Austria, 2023.","apa":"Marveggio, A. (2023). Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587","chicago":"Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587."},"type":"dissertation","title":"Weak-strong stability and phase-field approximation of interface evolution problems in fluid mechanics and in material sciences","department":[{"_id":"GradSch"},{"_id":"JuFi"}],"date_published":"2023-11-21T00:00:00Z","has_accepted_license":"1","abstract":[{"lang":"eng","text":"This thesis concerns the application of variational methods to the study of evolution problems arising in fluid mechanics and in material sciences. The main focus is on weak-strong stability properties of some curvature driven interface evolution problems, such as the two-phase Navier–Stokes flow with surface tension and multiphase mean curvature flow, and on the phase-field approximation of the latter. Furthermore, we discuss a variational approach to the study of a class of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes flow with surface tension within a bounded domain. The two fluids are immiscible and separated by a sharp interface, which intersects the boundary of the domain at a constant contact angle of ninety degree. We devise a suitable concept of varifolds solutions for the associated interface evolution problem and we establish a weak-strong uniqueness principle in case of a two dimensional ambient space. In order to focus on the boundary effects and on the singular geometry of the evolving domains, we work for simplicity in the regime of same viscosities for the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow for a suitable class of multi- well potentials and for well-prepared initial data. We even establish a rate of convergence. Our relative energy approach relies on the concept of gradient-flow calibration for branching singularities in multiphase mean curvature flow and thus enables us to overcome the limitations of other approaches. To the best of the author’s knowledge, our result is the first quantitative and unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis thesis also contains a first study of weak-strong stability for planar multiphase mean curvature flow beyond the singularity resulting from a topology change. Previous weak-strong results are indeed limited to time horizons before the first topology change of the strong solution. We consider circular topology changes and we prove weak-strong stability for BV solutions to planar multiphase mean curvature flow beyond the associated singular times by dynamically adapting the strong solutions to the weak one by means of a space-time shift.\r\nIn the context of interface evolution problems, our proofs for the main results of this thesis are based on the relative energy technique, relying on novel suitable notions of relative energy functionals, which in particular measure the interface error. Our statements follow from the resulting stability estimates for the relative energy associated to the problem.\r\nAt last, we introduce a variational approach to the study of nonlinear evolution problems. This approach hinges on the minimization of a parameter dependent family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy (WIDE) functionals. We consider a class of doubly nonlinear wave equations and establish the convergence, up to subsequences, of the associated WIDE minimizers to a solution of the target problem as the parameter goes to zero."}],"publisher":"Institute of Science and Technology Austria","degree_awarded":"PhD","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","acknowledgement":"The research projects contained in this thesis have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819).","page":"228","month":"11","date_created":"2023-11-21T11:41:05Z","date_updated":"2026-04-07T13:28:13Z","_id":"14587","doi":"10.15479/at:ista:14587","status":"public","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1,"language":[{"iso":"eng"}]},{"day":"24","author":[{"full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","last_name":"Hensel","orcid":"0000-0001-7252-8072"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian","first_name":"Maximilian","last_name":"Moser"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"eissn":["1432-0835"],"issn":["0944-2669"]},"ddc":["510"],"file":[{"access_level":"open_access","file_id":"12320","file_name":"2022_Calculus_Hensel.pdf","creator":"dernst","date_created":"2023-01-20T08:56:01Z","date_updated":"2023-01-20T08:56:01Z","relation":"main_file","content_type":"application/pdf","checksum":"b2da020ce50440080feedabeab5b09c4","file_size":1278493,"success":1}],"article_processing_charge":"No","external_id":{"isi":["000844247300008"]},"publication":"Calculus of Variations and Partial Differential Equations","scopus_import":"1","file_date_updated":"2023-01-20T08:56:01Z","article_number":"201","intvolume":" 61","publication_status":"published","year":"2022","type":"journal_article","title":"Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime","citation":{"chicago":"Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus of Variations and Partial Differential Equations. Springer Nature, 2022. https://doi.org/10.1007/s00526-022-02307-3.","mla":"Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus of Variations and Partial Differential Equations, vol. 61, no. 6, 201, Springer Nature, 2022, doi:10.1007/s00526-022-02307-3.","ieee":"S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime,” Calculus of Variations and Partial Differential Equations, vol. 61, no. 6. Springer Nature, 2022.","short":"S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations 61 (2022).","apa":"Hensel, S., & Moser, M. (2022). Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-022-02307-3","ista":"Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. 61(6), 201.","ama":"Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary contact energy: The non-perturbative regime. Calculus of Variations and Partial Differential Equations. 2022;61(6). doi:10.1007/s00526-022-02307-3"},"abstract":[{"text":"We extend the recent rigorous convergence result of Abels and Moser (SIAM J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin boundary condition towards evolution by mean curvature flow with constant contact angle. More precisely, in the present work we manage to remove the perturbative assumption on the contact angle being close to 90∘. We establish under usual double-well type assumptions on the potential and for a certain class of boundary energy densities the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π). For a very specific form of the boundary energy density, we even obtain from our methods a sharp convergence rate of order ε; again for general contact angles α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic expansions and stability estimates for the linearized Allen–Cahn operator. Instead, we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233, 2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy technique. We develop a careful adaptation of their approach in order to encode the constant contact angle condition. In fact, we perform this task at the level of the notion of gradient flow calibrations. This concept was recently introduced in the context of weak-strong uniqueness for multiphase mean curvature flow by Fischer et al. (arXiv:2003.05478v2).","lang":"eng"}],"publisher":"Springer Nature","department":[{"_id":"JuFi"}],"quality_controlled":"1","date_published":"2022-08-24T00:00:00Z","has_accepted_license":"1","month":"08","oa_version":"Published Version","acknowledgement":"This Project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2047/1 - 390685813.\r\nOpen Access funding enabled and organized by Projekt DEAL.","issue":"6","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"article_type":"original","date_created":"2022-09-11T22:01:54Z","volume":61,"date_updated":"2025-04-14T07:53:59Z","doi":"10.1007/s00526-022-02307-3","_id":"12079","status":"public","isi":1},{"corr_author":"1","article_number":"93","file_date_updated":"2022-08-16T06:55:22Z","year":"2022","publication_status":"published","intvolume":" 24","external_id":{"arxiv":["2112.11154"],"isi":["000834834300001"]},"article_processing_charge":"No","file":[{"relation":"main_file","content_type":"application/pdf","checksum":"75c5f286300e6f0539cf57b4dba108d5","success":1,"file_size":2045570,"access_level":"open_access","file_id":"11848","creator":"cchlebak","file_name":"2022_JMathFluidMech_Hensel.pdf","date_updated":"2022-08-16T06:55:22Z","date_created":"2022-08-16T06:55:22Z"}],"scopus_import":"1","publication":"Journal of Mathematical Fluid Mechanics","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"project":[{"grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"eissn":["1422-6952"],"issn":["1422-6928"]},"ddc":["510"],"author":[{"full_name":"Hensel, Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","orcid":"0000-0001-7252-8072","first_name":"Sebastian"},{"first_name":"Alice","last_name":"Marveggio","full_name":"Marveggio, Alice","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"14587"}]},"day":"01","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00021-022-00722-2","_id":"11842","status":"public","isi":1,"date_created":"2022-08-14T22:01:45Z","volume":24,"date_updated":"2026-04-07T13:28:13Z","month":"08","issue":"3","acknowledgement":"The authors warmly thank their former resp. current PhD advisor Julian Fischer for the suggestion of this problem and for valuable initial discussions on the subjects of this paper. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","oa_version":"Published Version","abstract":[{"text":"We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier–Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With respect to the motion of the interface, we consider pure transport by the fluid flow. Along the boundary of the domain, a complete slip boundary condition for the fluid velocities and a constant ninety degree contact angle condition for the interface are assumed. In the present work, we devise for the resulting evolution problem a suitable weak solution concept based on the framework of varifolds and establish as the main result a weak-strong uniqueness principle in 2D. The proof is based on a relative entropy argument and requires a non-trivial further development of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech. Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects of the necessarily singular geometry of the evolving fluid domains, we work for simplicity in the regime of same viscosities for the two fluids.","lang":"eng"}],"publisher":"Springer Nature","date_published":"2022-08-01T00:00:00Z","has_accepted_license":"1","department":[{"_id":"JuFi"}],"quality_controlled":"1","type":"journal_article","title":"Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities","citation":{"apa":"Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2","ieee":"S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities,” Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature, 2022.","mla":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature, 2022, doi:10.1007/s00021-022-00722-2.","short":"S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).","chicago":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature, 2022. https://doi.org/10.1007/s00021-022-00722-2.","ama":"Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2","ista":"Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 24(3), 93."},"arxiv":1},{"corr_author":"1","article_number":"2203.17143","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"year":"2022","_id":"14597","doi":"10.48550/ARXIV.2203.17143","publication_status":"draft","status":"public","date_created":"2023-11-23T09:30:02Z","date_updated":"2026-04-07T13:28:13Z","external_id":{"arxiv":["2203.17143"]},"article_processing_charge":"No","month":"03","publication":"arXiv","oa_version":"Preprint","ec_funded":1,"abstract":[{"text":"Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: As long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen-Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the gradient flow structure of the Allen-Cahn equation and its limiting motion: Building on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn operator or additional convergence hypotheses for the energy at positive times.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2203.17143"}],"date_published":"2022-03-31T00:00:00Z","project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"department":[{"_id":"JuFi"}],"author":[{"first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L"},{"full_name":"Marveggio, Alice","id":"25647992-AA84-11E9-9D75-8427E6697425","first_name":"Alice","last_name":"Marveggio"}],"type":"preprint","day":"31","related_material":{"record":[{"id":"17481","status":"public","relation":"later_version"},{"relation":"dissertation_contains","status":"public","id":"14587"}]},"title":"Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow","citation":{"chicago":"Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2203.17143.","mla":"Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, 2203.17143, doi:10.48550/ARXIV.2203.17143.","short":"J.L. Fischer, A. Marveggio, ArXiv (n.d.).","apa":"Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. https://doi.org/10.48550/ARXIV.2203.17143","ieee":"J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. .","ista":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv, 2203.17143.","ama":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143"},"arxiv":1},{"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","first_name":"Sebastian"}],"day":"14","related_material":{"record":[{"status":"public","id":"10012","relation":"part_of_dissertation"},{"id":"10013","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"7489"}]},"ddc":["515"],"project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials"}],"publication_identifier":{"issn":["2663-337X"]},"ec_funded":1,"article_processing_charge":"No","file":[{"file_size":15022154,"checksum":"c8475faaf0b680b4971f638f1db16347","content_type":"application/x-zip-compressed","relation":"source_file","date_updated":"2021-09-15T14:37:30Z","date_created":"2021-09-13T11:03:24Z","creator":"shensel","file_name":"thesis_final_Hensel.zip","file_id":"10008","access_level":"closed"},{"relation":"main_file","content_type":"application/pdf","checksum":"1a609937aa5275452822f45f2da17f07","file_size":6583638,"access_level":"open_access","file_id":"10014","file_name":"thesis_final_Hensel.pdf","creator":"shensel","date_updated":"2021-09-14T09:52:47Z","date_created":"2021-09-13T14:18:56Z"}],"supervisor":[{"last_name":"Fischer","orcid":"0000-0002-0479-558X","first_name":"Julian L","full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"year":"2021","publication_status":"published","corr_author":"1","file_date_updated":"2021-09-15T14:37:30Z","OA_place":"publisher","citation":{"ista":"Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria.","ama":"Hensel S. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. 2021. doi:10.15479/at:ista:10007","chicago":"Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10007.","ieee":"S. Hensel, “Curvature driven interface evolution: Uniqueness properties of weak solution concepts,” Institute of Science and Technology Austria, 2021.","short":"S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts, Institute of Science and Technology Austria, 2021.","mla":"Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10007.","apa":"Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007"},"title":"Curvature driven interface evolution: Uniqueness properties of weak solution concepts","type":"dissertation","has_accepted_license":"1","date_published":"2021-09-14T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"JuFi"}],"alternative_title":["ISTA Thesis"],"degree_awarded":"PhD","publisher":"Institute of Science and Technology Austria","abstract":[{"lang":"eng","text":"The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis."}],"oa_version":"Published Version","month":"09","page":"300","status":"public","doi":"10.15479/at:ista:10007","_id":"10007","date_updated":"2026-04-08T07:01:01Z","date_created":"2021-09-13T11:12:34Z","language":[{"iso":"eng"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa":1},{"publication":"arXiv","external_id":{"arxiv":["2108.01733"]},"article_processing_charge":"No","year":"2021","publication_status":"draft","corr_author":"1","article_number":"2108.01733","author":[{"first_name":"Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","full_name":"Hensel, Sebastian"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"}],"related_material":{"record":[{"status":"public","id":"13043","relation":"later_version"},{"id":"10007","status":"public","relation":"dissertation_contains"}]},"day":"03","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"ec_funded":1,"oa_version":"Preprint","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","month":"08","doi":"10.48550/arXiv.2108.01733","_id":"10013","status":"public","date_created":"2021-09-13T12:17:11Z","date_updated":"2026-04-08T07:01:01Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"citation":{"ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv. doi:10.48550/arXiv.2108.01733","ista":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv, 2108.01733.","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” arXiv. .","apa":"Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733","short":"S. Hensel, T. Laux, ArXiv (n.d.).","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733.","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733."},"arxiv":1,"type":"preprint","title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","main_file_link":[{"url":"https://arxiv.org/abs/2108.01733","open_access":"1"}],"date_published":"2021-08-03T00:00:00Z","department":[{"_id":"JuFi"}],"abstract":[{"text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.","lang":"eng"}]}]