[{"ddc":["510"],"acknowledgement":"FO and CW thank Ron Peled for insightful discussions on the white-noise multi-dimensional case in the Fall of 2023. CW thanks Barbara Dembin for the discussion during a workshop in Spring 2025. The work was done while the authors were affiliated with the Max Planck Institute for Mathematics in the Sciences; CW thanks the MPI for the support and warm hospitality. Open access funding provided by Institute of Science and Technology (IST Austria).","author":[{"full_name":"Otto, Felix","first_name":"Felix","last_name":"Otto"},{"last_name":"Palmieri","full_name":"Palmieri, Matteo","first_name":"Matteo"},{"first_name":"Christian","full_name":"Wagner, Christian","last_name":"Wagner","id":"bf0c729b-2619-11f0-8024-9d69bb2b8b20"}],"title":"On minimizing curves in a Brownian potential","article_processing_charge":"Yes (via OA deal)","date_published":"2026-02-14T00:00:00Z","oa_version":"Published Version","year":"2026","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Probability Theory and Related Fields","OA_place":"publisher","publisher":"Springer Nature","corr_author":"1","has_accepted_license":"1","status":"public","month":"02","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-026-01468-y"}],"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"doi":"10.1007/s00440-026-01468-y","department":[{"_id":"JuFi"}],"publication_status":"epub_ahead","date_created":"2026-03-02T10:05:23Z","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"day":"14","article_type":"original","abstract":[{"text":"We study a (1 + 1)-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical 2-dimensional random field Ising model. The scaling of the correlation length of the latter was recently characterized in Probab. Duke Math. J. 172(9), 1781–1811 (2023) and arXiv:2011.08768v3, (2022); our analysis is reminiscent of the multi-scale approach of the latter work and of Combinatorica 9, 161–187 (1989) . We show that at every dyadic scale from the system size down to the lattice spacing the minimizer contains at most order-one Dirichlet energy per unit length. We also establish a quenched homogenization result in the sense that the leading order of the minimal energy becomes deterministic as the ratio system size / lattice spacing diverges. To this purpose we adapt arguments from arXiv:2401.06768, (2024) on the (d + 1)-dimensional version our the model, with a Brownian replacing the white noise potential, to obtain the initial large-scale bounds. Based on our estimate of the (p = 3)-Dirichlet energy, we give an informal justification of the geometric linearization. Our bounds, which are oblivious to the microscopic cut-off scale provided by the lattice spacing, yield tightness of the law of minimizers in the space of continuous functions as the lattice spacing is sent to zero.","lang":"eng"}],"language":[{"iso":"eng"}],"oa":1,"OA_type":"hybrid","scopus_import":"1","_id":"21379","citation":{"ista":"Otto F, Palmieri M, Wagner C. 2026. On minimizing curves in a Brownian potential. Probability Theory and Related Fields.","apa":"Otto, F., Palmieri, M., & Wagner, C. (2026). On minimizing curves in a Brownian potential. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-026-01468-y","ama":"Otto F, Palmieri M, Wagner C. On minimizing curves in a Brownian potential. Probability Theory and Related Fields. 2026. doi:10.1007/s00440-026-01468-y","mla":"Otto, Felix, et al. “On Minimizing Curves in a Brownian Potential.” Probability Theory and Related Fields, Springer Nature, 2026, doi:10.1007/s00440-026-01468-y.","ieee":"F. Otto, M. Palmieri, and C. Wagner, “On minimizing curves in a Brownian potential,” Probability Theory and Related Fields. Springer Nature, 2026.","chicago":"Otto, Felix, Matteo Palmieri, and Christian Wagner. “On Minimizing Curves in a Brownian Potential.” Probability Theory and Related Fields. Springer Nature, 2026. https://doi.org/10.1007/s00440-026-01468-y.","short":"F. Otto, M. Palmieri, C. Wagner, Probability Theory and Related Fields (2026)."},"quality_controlled":"1","date_updated":"2026-03-02T15:15:13Z"},{"ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"file_date_updated":"2026-05-21T07:11:27Z","abstract":[{"lang":"eng","text":"The Dean–Kawasaki equation—one of the most fundamental SPDEs of\r\nfluctuating hydrodynamics—has been proposed as a model for density fluctuations in weakly interacting particle systems. In its original form, it is highly\r\nsingular and fails to be renormalizable, even by approaches such as regularity structures and paracontrolled distributions, hindering mathematical approaches to its rigorous justification. It has been understood recently that it is\r\nnatural to introduce a suitable regularization, for example, by applying a formal spatial discretization or by truncating high-frequency noise: This yields\r\nwell-posed equations that should still precisely approximate the law of the\r\nparticle density fluctuations.\r\nIn the present work, we prove that a regularization in the form of a formal\r\ndiscretization of the Dean–Kawasaki equation indeed accurately describes\r\ndensity fluctuations in systems of weakly interacting diffusing particles: We\r\nshow that, in suitable weak metrics, the law of fluctuations as predicted by\r\nthe discretized Dean–Kawasaki SPDE approximates the law of fluctuations\r\nof the original particle system, up to an error that is of arbitrarily high order in\r\nthe inverse particle number and a discretization error. In particular, the Dean–\r\nKawasaki equation provides a means for efficient and accurate simulations of\r\ndensity fluctuations in weakly interacting particle systems."}],"scopus_import":"1","OA_type":"hybrid","issue":"1","_id":"21894","quality_controlled":"1","citation":{"chicago":"Cornalba, Federico, Julian L Fischer, Jonas Ingmanns, and Claudia Raithel. “Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki Equation.” The Annals of Probability. Institute of Mathematical Statistics, 2026. https://doi.org/10.1214/25-aop1763.","short":"F. Cornalba, J.L. Fischer, J. Ingmanns, C. Raithel, The Annals of Probability 54 (2026) 155–215.","mla":"Cornalba, Federico, et al. “Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki Equation.” The Annals of Probability, vol. 54, no. 1, Institute of Mathematical Statistics, 2026, pp. 155–215, doi:10.1214/25-aop1763.","ieee":"F. Cornalba, J. L. Fischer, J. Ingmanns, and C. Raithel, “Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation,” The Annals of Probability, vol. 54, no. 1. Institute of Mathematical Statistics, pp. 155–215, 2026.","apa":"Cornalba, F., Fischer, J. L., Ingmanns, J., & Raithel, C. (2026). Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aop1763","ama":"Cornalba F, Fischer JL, Ingmanns J, Raithel C. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals of Probability. 2026;54(1):155-215. doi:10.1214/25-aop1763","ista":"Cornalba F, Fischer JL, Ingmanns J, Raithel C. 2026. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals of Probability. 54(1), 155–215."},"date_updated":"2026-05-21T07:21:25Z","APC_amount":"1352,08 EUR","file":[{"creator":"dernst","file_size":865745,"date_created":"2026-05-21T07:11:27Z","relation":"main_file","file_id":"21906","access_level":"open_access","success":1,"checksum":"3e60c0e25a1c96342029a7d2b031505f","file_name":"2026_AnnalsProbability_Cornalba.pdf","date_updated":"2026-05-21T07:11:27Z","content_type":"application/pdf"}],"department":[{"_id":"JuFi"}],"doi":"10.1214/25-aop1763","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"date_created":"2026-05-20T08:25:25Z","publication_status":"published","PlanS_conform":"1","day":"01","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"article_type":"original","publisher":"Institute of Mathematical Statistics","OA_place":"publisher","publication":"The Annals of Probability","status":"public","has_accepted_license":"1","arxiv":1,"corr_author":"1","keyword":["Weakly interacting particle systems","fluctuating hydrodynamics","Dean-Kawasaki equation","stochastic PDEs","numerical approximation"],"month":"01","intvolume":" 54","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"external_id":{"arxiv":["2303.00429"]},"ddc":["510"],"author":[{"first_name":"Federico","full_name":"Cornalba, Federico","last_name":"Cornalba"},{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","first_name":"Julian L","last_name":"Fischer"},{"orcid":"0009-0008-1310-7946","id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","last_name":"Ingmanns","full_name":"Ingmanns, Jonas","first_name":"Jonas"},{"full_name":"Raithel, Claudia","first_name":"Claudia","last_name":"Raithel"}],"acknowledgement":"All authors gratefully acknowledge funding from the Austrian Science Fund (FWF) through the project F65. CR gratefully acknowledges support from the Austrian Science Fund (FWF), grants P30000, P33010, W1245. FC gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411.","article_processing_charge":"Yes (in subscription journal)","title":"Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2026","page":"155-215","oa_version":"Published Version","volume":54,"date_published":"2026-01-01T00:00:00Z"},{"has_accepted_license":"1","status":"public","arxiv":1,"corr_author":"1","publisher":"Society for Industrial and Applied Mathematics","publication":"SIAM Journal on Numerical Analysis","OA_place":"publisher","publication_identifier":{"issn":["0036-1429"],"eissn":["1095-7170"]},"month":"02","intvolume":" 63","acknowledgement":"The work of the authors was supported by the Austrian Science Fund (FWF) projectF65.","author":[{"orcid":"0000-0002-6269-5149","id":"2CEB641C-A400-11E9-A717-D712E6697425","last_name":"Cornalba","first_name":"Federico","full_name":"Cornalba, Federico"},{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","full_name":"Fischer, Julian L","first_name":"Julian L"}],"ddc":["510"],"external_id":{"arxiv":["2311.08872"],"isi":["001447583400011"]},"page":"262-287","year":"2025","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2025-02-01T00:00:00Z","oa_version":"Published Version","volume":63,"article_processing_charge":"Yes (in subscription journal)","title":"Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics","OA_type":"hybrid","scopus_import":"1","abstract":[{"text":"Stochastic PDEs of fluctuating hydrodynamics are a powerful tool for the description of fluctuations in many-particle systems. In this paper, we develop and analyze a multilevel Monte Carlo (MLMC) scheme for the Dean–Kawasaki equation, a pivotal representative of this class of SPDEs. We prove analytically and demonstrate numerically that our MLMC scheme provides a significant reduction in computational cost (with respect to a standard Monte Carlo method) in the simulation of the Dean–Kawasaki equation. Specifically, we link this reduction in cost to having a sufficiently large average particle density and show that sizeable cost reductions can be obtained even when we have solutions with regions of low density. Numerical simulations are provided in the two-dimensional case, confirming our theoretical predictions. Our results are formulated entirely in terms of the law of distributions rather than in terms of strong spatial norms: this crucially allows for MLMC speed-ups altogether despite the Dean–Kawasaki equation being highly singular.","lang":"eng"}],"oa":1,"file_date_updated":"2025-02-17T08:32:23Z","language":[{"iso":"eng"}],"date_updated":"2025-09-30T10:30:31Z","quality_controlled":"1","citation":{"ieee":"F. Cornalba and J. L. Fischer, “Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics,” SIAM Journal on Numerical Analysis, vol. 63, no. 1. Society for Industrial and Applied Mathematics, pp. 262–287, 2025.","mla":"Cornalba, Federico, and Julian L. Fischer. “Multilevel Monte Carlo Methods for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” SIAM Journal on Numerical Analysis, vol. 63, no. 1, Society for Industrial and Applied Mathematics, 2025, pp. 262–87, doi:10.1137/23M1617345.","short":"F. Cornalba, J.L. Fischer, SIAM Journal on Numerical Analysis 63 (2025) 262–287.","chicago":"Cornalba, Federico, and Julian L Fischer. “Multilevel Monte Carlo Methods for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics, 2025. https://doi.org/10.1137/23M1617345.","ista":"Cornalba F, Fischer JL. 2025. Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis. 63(1), 262–287.","ama":"Cornalba F, Fischer JL. Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis. 2025;63(1):262-287. doi:10.1137/23M1617345","apa":"Cornalba, F., & Fischer, J. L. (2025). Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1617345"},"_id":"19027","issue":"1","publication_status":"published","date_created":"2025-02-16T23:02:34Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","doi":"10.1137/23M1617345","department":[{"_id":"JuFi"}],"file":[{"date_created":"2025-02-17T08:32:23Z","file_size":2435019,"creator":"dernst","relation":"main_file","file_id":"19029","date_updated":"2025-02-17T08:32:23Z","file_name":"2025_SIAMNumerAnaly_Cornalba.pdf","checksum":"53505647e848ed50f7e0d00c369b14e7","access_level":"open_access","success":1,"content_type":"application/pdf"}],"article_type":"original","day":"01","isi":1,"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}]},{"isi":1,"day":"01","project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"article_type":"original","doi":"10.1214/24-AAP2124","department":[{"_id":"JuFi"}],"type":"journal_article","date_created":"2025-04-06T22:01:32Z","publication_status":"published","_id":"19505","issue":"1","citation":{"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.","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","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","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.","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."},"date_updated":"2025-09-30T11:23:58Z","quality_controlled":"1","ec_funded":1,"language":[{"iso":"eng"}],"oa":1,"abstract":[{"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.","lang":"eng"}],"scopus_import":"1","OA_type":"green","article_processing_charge":"No","title":"The stochastic primitive equations with nonisothermal turbulent pressure","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2025","page":"635-700","date_published":"2025-02-01T00:00:00Z","volume":35,"oa_version":"Preprint","external_id":{"isi":["001434322900016"],"arxiv":["2210.05973"]},"author":[{"orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio"},{"last_name":"Hieber","full_name":"Hieber, Matthias","first_name":"Matthias"},{"first_name":"Amru","full_name":"Hussein, Amru","last_name":"Hussein"},{"last_name":"Saal","first_name":"Martin","full_name":"Saal, Martin"}],"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.","month":"02","intvolume":" 35","publication_identifier":{"issn":["1050-5164"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.05973","open_access":"1"}],"publisher":"Institute of Mathematical Statistics","OA_place":"repository","publication":"Annals of Applied Probability","status":"public","arxiv":1},{"ec_funded":1,"abstract":[{"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.","lang":"eng"}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-06-03T09:12:22Z","OA_type":"hybrid","scopus_import":"1","_id":"19783","issue":"2","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.","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.","short":"C. Hurm, M. Moser, GAMM-Mitteilungen 48 (2025).","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.","ista":"Hurm C, Moser M. 2025. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model. GAMM-Mitteilungen. 48(2), e70003.","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","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"},"date_updated":"2025-06-03T09:14:17Z","quality_controlled":"1","department":[{"_id":"JuFi"}],"doi":"10.1002/gamm.70003","file":[{"content_type":"application/pdf","checksum":"6bac9d3e566b68519ae80ac8b0f41f20","success":1,"access_level":"open_access","date_updated":"2025-06-03T09:12:22Z","file_name":"2025_GAMM_Hurm.pdf","file_id":"19786","relation":"main_file","creator":"dernst","date_created":"2025-06-03T09:12:22Z","file_size":513741}],"date_created":"2025-06-03T08:58:01Z","publication_status":"published","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"day":"01","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"article_type":"original","publisher":"Wiley","publication":"GAMM-Mitteilungen","OA_place":"publisher","has_accepted_license":"1","status":"public","arxiv":1,"month":"06","intvolume":" 48","publication_identifier":{"eissn":["1522-2608"],"issn":["0936-7195"]},"article_number":"e70003","ddc":["510"],"external_id":{"arxiv":["2402.13790"]},"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.","author":[{"full_name":"Hurm, Christoph","first_name":"Christoph","last_name":"Hurm"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","full_name":"Moser, Maximilian","first_name":"Maximilian","last_name":"Moser"}],"article_processing_charge":"Yes (via OA deal)","title":"Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-06-01T00:00:00Z","volume":48,"oa_version":"Published Version"},{"type":"journal_article","publication_status":"published","date_created":"2021-09-13T12:17:10Z","department":[{"_id":"JuFi"}],"doi":"10.4310/jdg/1747065796","article_type":"original","project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"day":"01","scopus_import":"1","OA_type":"green","language":[{"iso":"eng"}],"oa":1,"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"}],"ec_funded":1,"quality_controlled":"1","date_updated":"2026-07-06T13:37:21Z","citation":{"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 of Boston, 2025. https://doi.org/10.4310/jdg/1747065796.","short":"S. Hensel, T. Laux, Journal of Differential Geometry 130 (2025) 209–268.","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 of Boston, 2025, pp. 209–68, doi:10.4310/jdg/1747065796.","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 of Boston, pp. 209–268, 2025.","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 of Boston. 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."},"_id":"10011","author":[{"last_name":"Hensel","first_name":"Sebastian","full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Laux","first_name":"Tim","full_name":"Laux, Tim"}],"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.","external_id":{"arxiv":["2109.04233"]},"oa_version":"Preprint","date_published":"2025-05-01T00:00:00Z","volume":130,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","page":"209-268","title":"A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness","article_processing_charge":"No","corr_author":"1","arxiv":1,"status":"public","OA_place":"repository","publication":"Journal of Differential Geometry","publisher":"International Press of Boston","das_tickbox":"1","publication_identifier":{"issn":["0022-040X"],"eissn":["1945-743X"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2109.04233"}],"intvolume":" 130","keyword":["Mean curvature flow","gradient flows","varifolds","weak solutions","weak-strong uniqueness","calibrated geometry","gradient-flow calibrations"],"month":"05"},{"year":"2024","page":"53-133","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":12,"oa_version":"Published Version","date_published":"2024-03-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","title":"The stochastic primitive equations with transport noise and turbulent pressure","acknowledgement":"The authors thank the anonymous referees for their helpful comments and suggestions. Open Access funding enabled and organized by Projekt DEAL.","author":[{"last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Hieber","full_name":"Hieber, Matthias","first_name":"Matthias"},{"last_name":"Hussein","first_name":"Amru","full_name":"Hussein, Amru"},{"last_name":"Saal","full_name":"Saal, Martin","first_name":"Martin"}],"ddc":["510"],"external_id":{"isi":["000874389000001"],"arxiv":["2109.09561"]},"publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]},"month":"03","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"intvolume":" 12","has_accepted_license":"1","status":"public","arxiv":1,"publisher":"Springer Nature","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","article_type":"original","isi":1,"day":"01","publication_status":"published","date_created":"2023-01-12T12:12:29Z","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"department":[{"_id":"JuFi"}],"doi":"10.1007/s40072-022-00277-3","file":[{"content_type":"application/pdf","date_updated":"2024-07-22T09:29:48Z","file_name":"2024_StochasticsEquations_Agresti.pdf","checksum":"59c9000761134d681bdf9d482664044c","success":1,"access_level":"open_access","file_id":"17297","relation":"main_file","date_created":"2024-07-22T09:29:48Z","file_size":1206413,"creator":"dernst"}],"citation":{"apa":"Agresti, A., Hieber, M., Hussein, A., & Saal, M. (2024). The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00277-3","ama":"Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations. 2024;12:53-133. doi:10.1007/s40072-022-00277-3","ista":"Agresti A, Hieber M, Hussein A, Saal M. 2024. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations. 12, 53–133.","chicago":"Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2024. https://doi.org/10.1007/s40072-022-00277-3.","short":"A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024) 53–133.","mla":"Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 12, Springer Nature, 2024, pp. 53–133, doi:10.1007/s40072-022-00277-3.","ieee":"A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with transport noise and turbulent pressure,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 12. Springer Nature, pp. 53–133, 2024."},"quality_controlled":"1","date_updated":"2024-07-22T09:30:40Z","_id":"12178","scopus_import":"1","abstract":[{"lang":"eng","text":"In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well."}],"oa":1,"file_date_updated":"2024-07-22T09:29:48Z","language":[{"iso":"eng"}]},{"article_type":"original","project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"day":"01","isi":1,"date_created":"2023-02-02T10:45:15Z","publication_status":"published","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","doi":"10.1007/s00440-023-01249-x","department":[{"_id":"JuFi"}],"file":[{"content_type":"application/pdf","file_name":"2024_ProbTheory_Agresti.pdf","date_updated":"2024-07-22T09:21:09Z","success":1,"access_level":"open_access","checksum":"b8572339dbc5b8de4934dc5fd34afc7d","file_id":"17296","relation":"main_file","file_size":942801,"date_created":"2024-07-22T09:21:09Z","creator":"dernst"}],"citation":{"ista":"Agresti A, Veraar M. 2024. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. 188, 957–1015.","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","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","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.","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.","short":"A. Agresti, M. Veraar, Probability Theory and Related Fields 188 (2024) 957–1015.","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."},"date_updated":"2025-09-04T11:27:46Z","quality_controlled":"1","_id":"12485","scopus_import":"1","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2024-07-22T09:21:09Z","language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"volume":188,"date_published":"2024-04-01T00:00:00Z","oa_version":"Published Version","page":"957-1015","year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"The critical variational setting for stochastic evolution equations","article_processing_charge":"Yes (in subscription journal)","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).","author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962","first_name":"Antonio","full_name":"Agresti, Antonio","last_name":"Agresti"},{"first_name":"Mark","full_name":"Veraar, Mark","last_name":"Veraar"}],"ddc":["510"],"external_id":{"isi":["001154226500001"],"arxiv":["2206.00230"]},"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"intvolume":" 188","month":"04","arxiv":1,"has_accepted_license":"1","status":"public","publication":"Probability Theory and Related Fields","publisher":"Springer Nature"},{"publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]},"month":"09","intvolume":" 12","status":"public","has_accepted_license":"1","arxiv":1,"corr_author":"1","publisher":"Springer Nature","OA_place":"publisher","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","page":"1907-1981","oa_version":"Published Version","date_published":"2024-09-01T00:00:00Z","volume":12,"pmid":1,"article_processing_charge":"No","title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations","author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","first_name":"Antonio","last_name":"Agresti"}],"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. ","external_id":{"arxiv":["2207.08293"],"pmid":["39104877"],"isi":["001108594600001"]},"ddc":["510"],"quality_controlled":"1","date_updated":"2025-08-05T13:23:09Z","citation":{"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","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.","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.","short":"A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024) 1907–1981.","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.","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."},"_id":"12486","scopus_import":"1","OA_type":"hybrid","ec_funded":1,"file_date_updated":"2025-01-09T08:01:02Z","oa":1,"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"article_type":"original","isi":1,"day":"01","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","date_created":"2023-02-02T10:45:47Z","publication_status":"published","file":[{"creator":"dernst","file_size":1320682,"date_created":"2025-01-09T08:01:02Z","relation":"main_file","file_id":"18787","access_level":"open_access","success":1,"checksum":"3c93d07a5f7e0b0caa8062eadcfa69c2","file_name":"2024_StochPartDiffEquations_Agresti.pdf","date_updated":"2025-01-09T08:01:02Z","content_type":"application/pdf"}],"department":[{"_id":"JuFi"}],"doi":"10.1007/s40072-023-00319-4"},{"file":[{"access_level":"open_access","success":1,"checksum":"ec0582e2b55e2703a7da2686ae0d682e","file_name":"2024_FoundCompMath_Clozeau.pdf","date_updated":"2025-01-09T07:36:57Z","content_type":"application/pdf","creator":"dernst","file_size":1454406,"date_created":"2025-01-09T07:36:57Z","file_id":"18782","relation":"main_file"}],"doi":"10.1007/s10208-023-09613-y","department":[{"_id":"JuFi"}],"type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2023-06-11T22:00:40Z","day":"01","isi":1,"article_type":"original","file_date_updated":"2025-01-09T07:36:57Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"text":"We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory of homogenization, the method proceeds by computing d=3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L−1). In case of a suitable periodization of ⟨⋅⟩\r\n, we rigorously show that it is O(L−d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩\r\n of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function.","lang":"eng"}],"scopus_import":"1","OA_type":"hybrid","_id":"13129","quality_controlled":"1","citation":{"short":"N. Clozeau, M. Josien, F. Otto, Q. Xu, Foundations of Computational Mathematics 24 (2024) 1305–1387.","chicago":"Clozeau, Nicolas, Marc Josien, Felix Otto, and Qiang Xu. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics. Springer Nature, 2024. https://doi.org/10.1007/s10208-023-09613-y.","ieee":"N. Clozeau, M. Josien, F. Otto, and Q. Xu, “Bias in the representative volume element method: Periodize the ensemble instead of its realizations,” Foundations of Computational Mathematics, vol. 24. Springer Nature, pp. 1305–1387, 2024.","mla":"Clozeau, Nicolas, et al. “Bias in the Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational Mathematics, vol. 24, Springer Nature, 2024, pp. 1305–87, doi:10.1007/s10208-023-09613-y.","ama":"Clozeau N, Josien M, Otto F, Xu Q. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. 2024;24:1305-1387. doi:10.1007/s10208-023-09613-y","apa":"Clozeau, N., Josien, M., Otto, F., & Xu, Q. (2024). Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-023-09613-y","ista":"Clozeau N, Josien M, Otto F, Xu Q. 2024. Bias in the representative volume element method: Periodize the ensemble instead of its realizations. Foundations of Computational Mathematics. 24, 1305–1387."},"date_updated":"2025-01-09T07:37:50Z","external_id":{"isi":["000999623100001"]},"ddc":["510"],"author":[{"id":"fea1b376-906f-11eb-847d-b2c0cf46455b","full_name":"Clozeau, Nicolas","first_name":"Nicolas","last_name":"Clozeau"},{"first_name":"Marc","full_name":"Josien, Marc","last_name":"Josien"},{"last_name":"Otto","full_name":"Otto, Felix","first_name":"Felix"},{"full_name":"Xu, Qiang","first_name":"Qiang","last_name":"Xu"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","title":"Bias in the representative volume element method: Periodize the ensemble instead of its realizations","article_processing_charge":"Yes (via OA deal)","date_published":"2024-08-01T00:00:00Z","volume":24,"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","page":"1305-1387","OA_place":"publisher","publication":"Foundations of Computational Mathematics","publisher":"Springer Nature","corr_author":"1","status":"public","has_accepted_license":"1","intvolume":" 24","month":"08","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]}},{"file":[{"content_type":"application/pdf","file_name":"2024_NeuralCompApplications_Cornalba.pdf","date_updated":"2024-07-16T08:08:54Z","success":1,"access_level":"open_access","checksum":"04573d8e74c6119b97c2ca0a984e19a1","relation":"main_file","file_id":"17251","file_size":4412285,"date_created":"2024-07-16T08:08:54Z","creator":"dernst"}],"department":[{"_id":"JuFi"}],"doi":"10.1007/s00521-023-09033-7","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2023-10-22T22:01:16Z","day":"01","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"article_type":"original","ec_funded":1,"file_date_updated":"2024-07-16T08:08:54Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"lang":"eng","text":"We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format."}],"scopus_import":"1","issue":"2","_id":"14451","citation":{"ieee":"F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading,” Neural Computing and Applications, vol. 36, no. 2. Springer Nature, pp. 617–637, 2024.","mla":"Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications, vol. 36, no. 2, Springer Nature, 2024, pp. 617–37, doi:10.1007/s00521-023-09033-7.","short":"F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications 36 (2024) 617–637.","chicago":"Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” Neural Computing and Applications. Springer Nature, 2024. https://doi.org/10.1007/s00521-023-09033-7.","ista":"Cornalba F, Disselkamp C, Scassola D, Helf C. 2024. Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. 36(2), 617–637.","ama":"Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. 2024;36(2):617-637. doi:10.1007/s00521-023-09033-7","apa":"Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2024). Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications. Springer Nature. https://doi.org/10.1007/s00521-023-09033-7"},"date_updated":"2025-04-23T07:39:14Z","quality_controlled":"1","external_id":{"arxiv":["2203.04579"],"pmid":["38187995"]},"ddc":["000"],"author":[{"first_name":"Federico","full_name":"Cornalba, Federico","last_name":"Cornalba","id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149"},{"full_name":"Disselkamp, Constantin","first_name":"Constantin","last_name":"Disselkamp"},{"last_name":"Scassola","full_name":"Scassola, Davide","first_name":"Davide"},{"first_name":"Christopher","full_name":"Helf, Christopher","last_name":"Helf"}],"acknowledgement":"Open access funding provided by Università degli Studi di Trieste within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.","article_processing_charge":"Yes (via OA deal)","title":"Multi-objective reward generalization: Improving performance of Deep Reinforcement Learning for applications in single-asset trading","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","page":"617-637","volume":36,"date_published":"2024-01-01T00:00:00Z","pmid":1,"oa_version":"Published Version","publisher":"Springer Nature","publication":"Neural Computing and Applications","status":"public","has_accepted_license":"1","corr_author":"1","arxiv":1,"month":"01","intvolume":" 36","publication_identifier":{"eissn":["1433-3058"],"issn":["0941-0643"]}},{"scopus_import":"1","OA_type":"hybrid","ec_funded":1,"file_date_updated":"2025-01-09T08:10:54Z","language":[{"iso":"eng"}],"oa":1,"abstract":[{"lang":"eng","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."}],"quality_controlled":"1","citation":{"short":"N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024) 485–541.","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.","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.","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.","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","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","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."},"date_updated":"2025-09-04T11:43:43Z","_id":"14797","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2024-01-14T23:00:57Z","file":[{"checksum":"34f44cad6a210ff66791ee37e590af2c","access_level":"open_access","success":1,"date_updated":"2025-01-09T08:10:54Z","file_name":"2024_ProbTheoryRelatFields_Clozeau.pdf","content_type":"application/pdf","creator":"dernst","date_created":"2025-01-09T08:10:54Z","file_size":880117,"relation":"main_file","file_id":"18788"}],"doi":"10.1007/s00440-023-01254-0","department":[{"_id":"JuFi"}],"article_type":"original","day":"01","isi":1,"project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"status":"public","has_accepted_license":"1","arxiv":1,"corr_author":"1","publisher":"Springer Nature","OA_place":"publisher","publication":"Probability Theory and Related Fields","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"month":"10","intvolume":" 190","author":[{"last_name":"Clozeau","first_name":"Nicolas","full_name":"Clozeau, Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b"},{"last_name":"Mattesini","first_name":"Francesco","full_name":"Mattesini, Francesco"}],"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.","external_id":{"isi":["001136206200002"],"arxiv":["2303.00353"]},"ddc":["510"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","page":"485-541","date_published":"2024-10-01T00:00:00Z","volume":190,"oa_version":"Published Version","article_processing_charge":"Yes (in subscription journal)","title":"Annealed quantitative estimates for the quadratic 2D-discrete random matching problem"},{"date_updated":"2025-09-04T11:54:01Z","quality_controlled":"1","citation":{"mla":"Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol. 34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3.","ieee":"E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science, vol. 34, no. 2. Springer Nature, 2024.","chicago":"Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3.","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","ista":"Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2), 30.","apa":"Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3","ama":"Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 2024;34(2). doi:10.1007/s00332-023-10005-3"},"issue":"2","_id":"14884","scopus_import":"1","oa":1,"language":[{"iso":"eng"}],"abstract":[{"text":"We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.","lang":"eng"}],"article_type":"original","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"isi":1,"day":"23","type":"journal_article","date_created":"2024-01-28T23:01:42Z","publication_status":"published","department":[{"_id":"JuFi"}],"doi":"10.1007/s00332-023-10005-3","publication_identifier":{"issn":["0938-8974"],"eissn":["1432-1467"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.05151","open_access":"1"}],"intvolume":" 34","month":"01","arxiv":1,"status":"public","publication":"Journal of Nonlinear Science","publisher":"Springer Nature","date_published":"2024-01-23T00:00:00Z","oa_version":"Preprint","volume":34,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","article_processing_charge":"No","author":[{"last_name":"Davoli","full_name":"Davoli, Elisa","first_name":"Elisa"},{"full_name":"D’Elia, Lorenza","first_name":"Lorenza","last_name":"D’Elia"},{"id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","last_name":"Ingmanns","full_name":"Ingmanns, Jonas","first_name":"Jonas"}],"acknowledgement":"All authors acknowledge support of the Austrian Science Fund (FWF) through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally been supported by the FWF through grants V662, Y1292, and P35359, as well as from OeAD through the WTZ grant CZ09/2023.","external_id":{"arxiv":["2306.05151"],"isi":["001147480200001"]},"article_number":"30"},{"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).","author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","first_name":"Antonio","last_name":"Agresti"},{"first_name":"Eliseo","full_name":"Luongo, Eliseo","last_name":"Luongo"}],"ddc":["510"],"external_id":{"isi":["001172711400002"],"pmid":["39351582"],"arxiv":["2306.11081"]},"volume":390,"pmid":1,"date_published":"2024-10-01T00:00:00Z","oa_version":"Published Version","year":"2024","page":"2727-2766","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions","article_processing_charge":"Yes (via OA deal)","arxiv":1,"has_accepted_license":"1","status":"public","publication":"Mathematische Annalen","OA_place":"publisher","publisher":"Springer Nature","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"intvolume":" 390","month":"10","publication_status":"published","date_created":"2024-03-10T23:00:54Z","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"doi":"10.1007/s00208-024-02812-0","department":[{"_id":"JuFi"}],"file":[{"content_type":"application/pdf","success":1,"access_level":"open_access","checksum":"d55cac8bddea09a97f06612825c4f229","file_name":"2024_MathAnnalen_Agresti.pdf","date_updated":"2025-01-09T08:23:36Z","relation":"main_file","file_id":"18790","creator":"dernst","file_size":661557,"date_created":"2025-01-09T08:23:36Z"}],"article_type":"original","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"day":"01","isi":1,"OA_type":"hybrid","scopus_import":"1","abstract":[{"lang":"eng","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."}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-01-09T08:23:36Z","ec_funded":1,"quality_controlled":"1","citation":{"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","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.","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.","short":"A. Agresti, E. Luongo, Mathematische Annalen 390 (2024) 2727–2766.","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.","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."},"date_updated":"2025-09-04T12:19:59Z","_id":"15098"},{"ec_funded":1,"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"}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2024-04-23T07:30:48Z","scopus_import":"1","issue":"4","_id":"15334","date_updated":"2025-09-04T13:45:40Z","citation":{"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.","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","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."},"quality_controlled":"1","doi":"10.1007/s00526-024-02715-7","department":[{"_id":"JuFi"}],"file":[{"relation":"main_file","file_id":"15343","date_created":"2024-04-23T07:30:48Z","file_size":975186,"creator":"dernst","content_type":"application/pdf","date_updated":"2024-04-23T07:30:48Z","file_name":"2024_CalculusEquations_Abels.pdf","checksum":"b1095fad4cae596f52cc616a973bdde2","success":1,"access_level":"open_access"}],"date_created":"2024-04-21T22:00:52Z","publication_status":"published","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","day":"01","isi":1,"project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"article_type":"original","publisher":"Springer Nature","publication":"Calculus of Variations and Partial Differential Equations","has_accepted_license":"1","status":"public","arxiv":1,"month":"05","intvolume":" 63","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"ddc":["510"],"article_number":"94","external_id":{"isi":["001199418100002"],"arxiv":["2304.12096"]},"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).","author":[{"first_name":"Helmut","full_name":"Abels, Helmut","last_name":"Abels"},{"last_name":"Fei","first_name":"Mingwen","full_name":"Fei, Mingwen"},{"id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","full_name":"Moser, Maximilian","first_name":"Maximilian"}],"article_processing_charge":"Yes (via OA deal)","title":"Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility","year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":63,"date_published":"2024-05-01T00:00:00Z","oa_version":"Published Version"},{"intvolume":" 73","month":"01","publication_identifier":{"issn":["0022-2518"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.11150"}],"OA_place":"repository","publication":"Indiana University Mathematics Journal","publisher":"Indiana University Mathematics Journal","corr_author":"1","arxiv":1,"status":"public","title":"BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness","article_processing_charge":"No","oa_version":"Preprint","date_published":"2024-01-01T00:00:00Z","volume":73,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024","page":"111-148","external_id":{"arxiv":["2112.11150"]},"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","first_name":"Sebastian","last_name":"Hensel"},{"last_name":"Laux","first_name":"Tim","full_name":"Laux, Tim"}],"_id":"18926","issue":"1","date_updated":"2025-01-27T15:23:57Z","quality_controlled":"1","citation":{"apa":"Hensel, S., & Laux, T. (2024). BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness. Indiana University Mathematics Journal. Indiana University Mathematics Journal. https://doi.org/10.1512/iumj.2024.73.9701","ama":"Hensel S, Laux T. BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness. Indiana University Mathematics Journal. 2024;73(1):111-148. doi:10.1512/iumj.2024.73.9701","ista":"Hensel S, Laux T. 2024. BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness. Indiana University Mathematics Journal. 73(1), 111–148.","chicago":"Hensel, Sebastian, and Tim Laux. “BV Solutions for Mean Curvature Flow with Constant Angle: Allen-Cahn Approximation and Weak-Strong Uniqueness.” Indiana University Mathematics Journal. Indiana University Mathematics Journal, 2024. https://doi.org/10.1512/iumj.2024.73.9701.","short":"S. Hensel, T. Laux, Indiana University Mathematics Journal 73 (2024) 111–148.","mla":"Hensel, Sebastian, and Tim Laux. “BV Solutions for Mean Curvature Flow with Constant Angle: Allen-Cahn Approximation and Weak-Strong Uniqueness.” Indiana University Mathematics Journal, vol. 73, no. 1, Indiana University Mathematics Journal, 2024, pp. 111–48, doi:10.1512/iumj.2024.73.9701.","ieee":"S. Hensel and T. Laux, “BV solutions for mean curvature flow with constant angle: Allen-Cahn approximation and weak-strong uniqueness,” Indiana University Mathematics Journal, vol. 73, no. 1. Indiana University Mathematics Journal, pp. 111–148, 2024."},"language":[{"iso":"eng"}],"oa":1,"abstract":[{"lang":"eng","text":"We study weak solutions to mean curvature flow satisfying Young’s angle condition for general contact angles α ∈ (0, π). First, we construct BV solutions by using the Allen-Cahn approximation with boundary contact energy as proposed by Owen and Sternberg. Second, we prove the weak-strong uniqueness and stability for this solution concept. The main ingredient for both results is a relative energy, which can also be interpreted as a tilt excess. "}],"scopus_import":"1","OA_type":"green","day":"01","article_type":"original","department":[{"_id":"JuFi"}],"doi":"10.1512/iumj.2024.73.9701","type":"journal_article","publication_status":"published","date_created":"2025-01-27T15:20:19Z"},{"type":"journal_article","date_created":"2024-08-04T22:01:21Z","publication_status":"published","department":[{"_id":"JuFi"}],"doi":"10.1137/23M1562482","article_type":"original","project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"isi":1,"day":"01","scopus_import":"1","language":[{"iso":"eng"}],"oa":1,"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"date_updated":"2025-09-08T08:46:57Z","citation":{"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.","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.","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.","short":"A. Agresti, M. Veraar, SIAM Journal on Mathematical Analysis 56 (2024) 4870–4927.","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.","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","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"},"quality_controlled":"1","issue":"4","_id":"17372","author":[{"full_name":"Agresti, Antonio","first_name":"Antonio","last_name":"Agresti","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962"},{"full_name":"Veraar, Mark","first_name":"Mark","last_name":"Veraar"}],"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).","external_id":{"isi":["001315424500021"],"arxiv":["2301.06897"]},"date_published":"2024-08-01T00:00:00Z","oa_version":"Preprint","volume":56,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","page":"4870-4927","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems","article_processing_charge":"No","corr_author":"1","arxiv":1,"status":"public","publication":"SIAM Journal on Mathematical Analysis","publisher":"Society for Industrial and Applied Mathematics","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.06897"}],"intvolume":" 56","month":"08"},{"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.","author":[{"id":"fea1b376-906f-11eb-847d-b2c0cf46455b","last_name":"Clozeau","first_name":"Nicolas","full_name":"Clozeau, Nicolas"},{"first_name":"Lihan","full_name":"Wang, Lihan","last_name":"Wang"}],"external_id":{"isi":["001285416500001"],"arxiv":["2309.06798"]},"year":"2024","page":"973-1029","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2024-09-01T00:00:00Z","oa_version":"Preprint","volume":22,"article_processing_charge":"No","title":"Artificial boundary conditions for random elliptic systems with correlated coefficient field","status":"public","corr_author":"1","arxiv":1,"publisher":"Society for Industrial and Applied Mathematics","publication":"Multiscale Modeling and Simulation","OA_place":"repository","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.06798","open_access":"1"}],"publication_identifier":{"issn":["1540-3459"],"eissn":["1540-3467"]},"month":"09","intvolume":" 22","publication_status":"published","date_created":"2024-08-25T22:01:08Z","type":"journal_article","doi":"10.1137/23M1603819","department":[{"_id":"JuFi"}],"article_type":"original","isi":1,"day":"01","project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020"}],"OA_type":"green","scopus_import":"1","ec_funded":1,"abstract":[{"lang":"eng","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."}],"language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","date_updated":"2025-09-08T09:01:00Z","citation":{"short":"N. Clozeau, L. Wang, Multiscale Modeling and Simulation 22 (2024) 973–1029.","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.","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.","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.","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","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","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."},"issue":"3","_id":"17462"},{"author":[{"last_name":"Fischer","full_name":"Fischer, Julian L","first_name":"Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Marveggio","full_name":"Marveggio, Alice","first_name":"Alice","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"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.","external_id":{"isi":["001293853900003"]},"ddc":["510"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","page":"1117-1178","volume":41,"oa_version":"Published Version","date_published":"2024-01-24T00:00:00Z","article_processing_charge":"Yes","title":"Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase mean curvature flow","status":"public","has_accepted_license":"1","corr_author":"1","publisher":"EMS Press","publication":"Annales de l'Institut Henri Poincare C","publication_identifier":{"eissn":["1873-1430"],"issn":["0294-1449"]},"month":"01","intvolume":" 41","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_status":"published","date_created":"2024-09-01T22:01:09Z","file":[{"success":1,"access_level":"open_access","checksum":"b5ad02d9abd5b4701269cd1ad0a1cc8f","file_name":"2024_AnnInstHPoincare_Fischer.pdf","date_updated":"2024-09-09T07:46:42Z","content_type":"application/pdf","creator":"dernst","file_size":1348896,"date_created":"2024-09-09T07:46:42Z","file_id":"17923","relation":"main_file"}],"department":[{"_id":"JuFi"}],"doi":"10.4171/AIHPC/109","article_type":"original","day":"24","isi":1,"project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials"}],"scopus_import":"1","ec_funded":1,"oa":1,"file_date_updated":"2024-09-09T07:46:42Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"related_material":{"record":[{"relation":"earlier_version","id":"14597","status":"public"}]},"citation":{"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.","short":"J.L. Fischer, A. Marveggio, Annales de l’Institut Henri Poincare C 41 (2024) 1117–1178.","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.","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.","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","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","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."},"quality_controlled":"1","date_updated":"2025-09-08T09:11:01Z","_id":"17481","issue":"5"},{"ddc":["510"],"article_number":"77","external_id":{"isi":["001305530600001"],"pmid":["39239088"],"arxiv":["2311.02997"]},"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.","author":[{"full_name":"Abels, Helmut","first_name":"Helmut","last_name":"Abels"},{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","first_name":"Julian L","full_name":"Fischer, Julian L","last_name":"Fischer"},{"first_name":"Maximilian","full_name":"Moser, Maximilian","last_name":"Moser","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c"}],"title":"Approximation of classical two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system","article_processing_charge":"Yes (via OA deal)","date_published":"2024-09-03T00:00:00Z","oa_version":"Published Version","volume":248,"pmid":1,"year":"2024","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Archive for Rational Mechanics and Analysis","publisher":"Springer Nature","arxiv":1,"has_accepted_license":"1","status":"public","intvolume":" 248","month":"09","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"department":[{"_id":"JuFi"}],"doi":"10.1007/s00205-024-02020-9","file":[{"creator":"dernst","file_size":811131,"date_created":"2024-09-09T08:43:32Z","relation":"main_file","file_id":"17938","success":1,"access_level":"open_access","checksum":"98493a05b84e4513b6394dfad4851ddf","file_name":"2024_ArchiveRatAnalysis_Abels.pdf","date_updated":"2024-09-09T08:43:32Z","content_type":"application/pdf"}],"publication_status":"published","date_created":"2024-09-08T22:01:10Z","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"day":"03","isi":1,"article_type":"original","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"}],"file_date_updated":"2024-09-09T08:43:32Z","language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"scopus_import":"1","issue":"5","_id":"17887","date_updated":"2025-09-08T09:11:41Z","citation":{"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","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","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.","short":"H. Abels, J.L. Fischer, M. Moser, Archive for Rational Mechanics and Analysis 248 (2024).","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.","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."},"quality_controlled":"1"}]