[{"OA_place":"repository","volume":35,"publication_identifier":{"issn":["1050-5164"]},"ec_funded":1,"status":"public","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.","type":"journal_article","month":"02","arxiv":1,"isi":1,"oa":1,"year":"2025","language":[{"iso":"eng"}],"page":"635-700","issue":"1","doi":"10.1214/24-AAP2124","quality_controlled":"1","citation":{"chicago":"Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Nonisothermal Turbulent Pressure.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/24-AAP2124\">https://doi.org/10.1214/24-AAP2124</a>.","ama":"Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with nonisothermal turbulent pressure. <i>Annals of Applied Probability</i>. 2025;35(1):635-700. doi:<a href=\"https://doi.org/10.1214/24-AAP2124\">10.1214/24-AAP2124</a>","apa":"Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2025). The stochastic primitive equations with nonisothermal turbulent pressure. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/24-AAP2124\">https://doi.org/10.1214/24-AAP2124</a>","ieee":"A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with nonisothermal turbulent pressure,” <i>Annals of Applied Probability</i>, vol. 35, no. 1. Institute of Mathematical Statistics, pp. 635–700, 2025.","short":"A. Agresti, M. Hieber, A. Hussein, M. Saal, Annals of Applied Probability 35 (2025) 635–700.","mla":"Agresti, Antonio, et al. “The Stochastic Primitive Equations with Nonisothermal Turbulent Pressure.” <i>Annals of Applied Probability</i>, vol. 35, no. 1, Institute of Mathematical Statistics, 2025, pp. 635–700, doi:<a href=\"https://doi.org/10.1214/24-AAP2124\">10.1214/24-AAP2124</a>.","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."},"publisher":"Institute of Mathematical Statistics","article_type":"original","scopus_import":"1","department":[{"_id":"JuFi"}],"intvolume":"        35","day":"01","article_processing_charge":"No","oa_version":"Preprint","_id":"19505","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819","name":"Bridging Scales in Random Materials","call_identifier":"H2020"}],"title":"The stochastic primitive equations with nonisothermal turbulent pressure","author":[{"full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","first_name":"Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962"},{"full_name":"Hieber, Matthias","first_name":"Matthias","last_name":"Hieber"},{"last_name":"Hussein","first_name":"Amru","full_name":"Hussein, Amru"},{"full_name":"Saal, Martin","first_name":"Martin","last_name":"Saal"}],"date_created":"2025-04-06T22:01:32Z","external_id":{"arxiv":["2210.05973"],"isi":["001434322900016"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.05973"}],"date_updated":"2025-09-30T11:23:58Z","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"}],"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Annals of Applied Probability","date_published":"2025-02-01T00:00:00Z","OA_type":"green"},{"doi":"10.1007/s40072-022-00277-3","has_accepted_license":"1","page":"53-133","file":[{"file_id":"17297","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","date_created":"2024-07-22T09:29:48Z","file_size":1206413,"content_type":"application/pdf","checksum":"59c9000761134d681bdf9d482664044c","date_updated":"2024-07-22T09:29:48Z","file_name":"2024_StochasticsEquations_Agresti.pdf"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2024","oa":1,"isi":1,"arxiv":1,"month":"03","license":"https://creativecommons.org/licenses/by/4.0/","type":"journal_article","acknowledgement":"The authors thank the anonymous referees for their helpful comments and suggestions. Open Access funding enabled and organized by Projekt DEAL.","status":"public","publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]},"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"volume":12,"date_published":"2024-03-01T00:00:00Z","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","file_date_updated":"2024-07-22T09:29:48Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","abstract":[{"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.","lang":"eng"}],"date_updated":"2024-07-22T09:30:40Z","external_id":{"isi":["000874389000001"],"arxiv":["2109.09561"]},"date_created":"2023-01-12T12:12:29Z","title":"The stochastic primitive equations with transport noise and turbulent pressure","author":[{"last_name":"Agresti","first_name":"Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","full_name":"Agresti, Antonio"},{"last_name":"Hieber","first_name":"Matthias","full_name":"Hieber, Matthias"},{"full_name":"Hussein, Amru","last_name":"Hussein","first_name":"Amru"},{"full_name":"Saal, Martin","first_name":"Martin","last_name":"Saal"}],"_id":"12178","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","day":"01","intvolume":"        12","department":[{"_id":"JuFi"}],"scopus_import":"1","article_type":"original","publisher":"Springer Nature","ddc":["510"],"citation":{"chicago":"Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s40072-022-00277-3\">https://doi.org/10.1007/s40072-022-00277-3</a>.","ama":"Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations with transport noise and turbulent pressure. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2024;12:53-133. doi:<a href=\"https://doi.org/10.1007/s40072-022-00277-3\">10.1007/s40072-022-00277-3</a>","apa":"Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2024). The stochastic primitive equations with transport noise and turbulent pressure. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-022-00277-3\">https://doi.org/10.1007/s40072-022-00277-3</a>","ieee":"A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive equations with transport noise and turbulent pressure,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 12. Springer Nature, pp. 53–133, 2024.","mla":"Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 12, Springer Nature, 2024, pp. 53–133, doi:<a href=\"https://doi.org/10.1007/s40072-022-00277-3\">10.1007/s40072-022-00277-3</a>.","short":"A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024) 53–133.","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."},"quality_controlled":"1"},{"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"ec_funded":1,"status":"public","volume":188,"type":"journal_article","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).","arxiv":1,"isi":1,"month":"04","page":"957-1015","has_accepted_license":"1","doi":"10.1007/s00440-023-01249-x","oa":1,"year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"date_created":"2024-07-22T09:21:09Z","relation":"main_file","file_name":"2024_ProbTheory_Agresti.pdf","date_updated":"2024-07-22T09:21:09Z","file_size":942801,"content_type":"application/pdf","checksum":"b8572339dbc5b8de4934dc5fd34afc7d","file_id":"17296","access_level":"open_access","creator":"dernst","success":1}],"language":[{"iso":"eng"}],"publisher":"Springer Nature","citation":{"apa":"Agresti, A., &#38; Veraar, M. (2024). The critical variational setting for stochastic evolution equations. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01249-x\">https://doi.org/10.1007/s00440-023-01249-x</a>","ama":"Agresti A, Veraar M. The critical variational setting for stochastic evolution equations. <i>Probability Theory and Related Fields</i>. 2024;188:957-1015. doi:<a href=\"https://doi.org/10.1007/s00440-023-01249-x\">10.1007/s00440-023-01249-x</a>","chicago":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01249-x\">https://doi.org/10.1007/s00440-023-01249-x</a>.","ista":"Agresti A, Veraar M. 2024. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. 188, 957–1015.","short":"A. Agresti, M. Veraar, Probability Theory and Related Fields 188 (2024) 957–1015.","mla":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” <i>Probability Theory and Related Fields</i>, vol. 188, Springer Nature, 2024, pp. 957–1015, doi:<a href=\"https://doi.org/10.1007/s00440-023-01249-x\">10.1007/s00440-023-01249-x</a>.","ieee":"A. Agresti and M. Veraar, “The critical variational setting for stochastic evolution equations,” <i>Probability Theory and Related Fields</i>, vol. 188. Springer Nature, pp. 957–1015, 2024."},"quality_controlled":"1","ddc":["510"],"day":"01","article_processing_charge":"Yes (in subscription journal)","oa_version":"Published Version","_id":"12485","article_type":"original","scopus_import":"1","department":[{"_id":"JuFi"}],"intvolume":"       188","date_updated":"2025-09-04T11:27:46Z","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"}],"project":[{"grant_number":"948819","name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"title":"The critical variational setting for stochastic evolution equations","author":[{"full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","first_name":"Antonio","orcid":"0000-0002-9573-2962"},{"last_name":"Veraar","first_name":"Mark","full_name":"Veraar, Mark"}],"external_id":{"isi":["001154226500001"],"arxiv":["2206.00230"]},"date_created":"2023-02-02T10:45:15Z","date_published":"2024-04-01T00:00:00Z","publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"Probability Theory and Related Fields","file_date_updated":"2024-07-22T09:21:09Z"},{"_id":"12486","oa_version":"Published Version","article_processing_charge":"No","day":"01","intvolume":"        12","department":[{"_id":"JuFi"}],"scopus_import":"1","article_type":"original","publisher":"Springer Nature","ddc":["510"],"quality_controlled":"1","citation":{"ama":"Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. 2024;12:1907-1981. doi:<a href=\"https://doi.org/10.1007/s40072-023-00319-4\">10.1007/s40072-023-00319-4</a>","apa":"Agresti, A. (2024). Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40072-023-00319-4\">https://doi.org/10.1007/s40072-023-00319-4</a>","chicago":"Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise for Systems of Reaction-Diffusion Equations.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s40072-023-00319-4\">https://doi.org/10.1007/s40072-023-00319-4</a>.","ista":"Agresti A. 2024. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations. 12, 1907–1981.","ieee":"A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations,” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 12. Springer Nature, pp. 1907–1981, 2024.","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.” <i>Stochastics and Partial Differential Equations: Analysis and Computations</i>, vol. 12, Springer Nature, 2024, pp. 1907–81, doi:<a href=\"https://doi.org/10.1007/s40072-023-00319-4\">10.1007/s40072-023-00319-4</a>."},"corr_author":"1","OA_type":"hybrid","date_published":"2024-09-01T00:00:00Z","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","file_date_updated":"2025-01-09T08:01:02Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"publication_status":"published","abstract":[{"text":"This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas.","lang":"eng"}],"date_updated":"2025-08-05T13:23:09Z","date_created":"2023-02-02T10:45:47Z","external_id":{"arxiv":["2207.08293"],"isi":["001108594600001"],"pmid":["39104877"]},"author":[{"first_name":"Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"}],"title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations","project":[{"call_identifier":"H2020","name":"Bridging Scales in Random Materials","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"type":"journal_article","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. ","status":"public","ec_funded":1,"publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"volume":12,"OA_place":"publisher","doi":"10.1007/s40072-023-00319-4","page":"1907-1981","has_accepted_license":"1","file":[{"relation":"main_file","date_created":"2025-01-09T08:01:02Z","date_updated":"2025-01-09T08:01:02Z","file_name":"2024_StochPartDiffEquations_Agresti.pdf","content_type":"application/pdf","file_size":1320682,"checksum":"3c93d07a5f7e0b0caa8062eadcfa69c2","file_id":"18787","creator":"dernst","success":1,"access_level":"open_access"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2024","oa":1,"isi":1,"arxiv":1,"month":"09"},{"ddc":["510"],"quality_controlled":"1","citation":{"apa":"Agresti, A., &#38; Luongo, E. (2024). Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-02812-0\">https://doi.org/10.1007/s00208-024-02812-0</a>","ama":"Agresti A, Luongo E. Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions. <i>Mathematische Annalen</i>. 2024;390:2727-2766. doi:<a href=\"https://doi.org/10.1007/s00208-024-02812-0\">10.1007/s00208-024-02812-0</a>","chicago":"Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-024-02812-0\">https://doi.org/10.1007/s00208-024-02812-0</a>.","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.","ieee":"A. Agresti and E. Luongo, “Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions,” <i>Mathematische Annalen</i>, vol. 390. Springer Nature, pp. 2727–2766, 2024.","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.” <i>Mathematische Annalen</i>, vol. 390, Springer Nature, 2024, pp. 2727–66, doi:<a href=\"https://doi.org/10.1007/s00208-024-02812-0\">10.1007/s00208-024-02812-0</a>."},"publisher":"Springer Nature","intvolume":"       390","department":[{"_id":"JuFi"}],"scopus_import":"1","article_type":"original","_id":"15098","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","day":"01","date_created":"2024-03-10T23:00:54Z","external_id":{"isi":["001172711400002"],"arxiv":["2306.11081"],"pmid":["39351582"]},"author":[{"orcid":"0000-0002-9573-2962","first_name":"Antonio","last_name":"Agresti","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","full_name":"Agresti, Antonio"},{"full_name":"Luongo, Eliseo","first_name":"Eliseo","last_name":"Luongo"}],"title":"Global well-posedness and interior regularity of 2D Navier-Stokes equations with stochastic boundary conditions","project":[{"name":"Bridging Scales in Random Materials","grant_number":"948819","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"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."}],"date_updated":"2025-09-04T12:19:59Z","publication":"Mathematische Annalen","file_date_updated":"2025-01-09T08:23:36Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","pmid":1,"OA_type":"hybrid","date_published":"2024-10-01T00:00:00Z","volume":390,"OA_place":"publisher","status":"public","ec_funded":1,"publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"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).","type":"journal_article","month":"10","isi":1,"arxiv":1,"file":[{"creator":"dernst","success":1,"access_level":"open_access","file_id":"18790","date_updated":"2025-01-09T08:23:36Z","file_name":"2024_MathAnnalen_Agresti.pdf","checksum":"d55cac8bddea09a97f06612825c4f229","content_type":"application/pdf","file_size":661557,"relation":"main_file","date_created":"2025-01-09T08:23:36Z"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2024","oa":1,"doi":"10.1007/s00208-024-02812-0","has_accepted_license":"1","page":"2727-2766"},{"date_published":"2024-02-01T00:00:00Z","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publication":"Annales de l'institut Henri Poincare Probability and Statistics","date_updated":"2024-10-09T21:08:30Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.01274"}],"abstract":[{"text":"In this paper we consider an SPDE where the leading term is a second order operator with periodic boundary conditions, coefficients which are measurable in  (t,ω) , and Hölder continuous in space. Assuming stochastic parabolicity conditions, we prove Lp((0,T)×Ω,tκdt;Hσ,q(Td)) -estimates. The main novelty is that we do not require  p=q . Moreover, we allow arbitrary  σ∈R  and weights in time. Such mixed regularity estimates play a crucial role in applications to nonlinear SPDEs which is clear from our previous work. To prove our main results we develop a general perturbation theory for SPDEs. Moreover, we prove a new result on pointwise multiplication in spaces with fractional smoothness.","lang":"eng"}],"date_created":"2024-03-17T23:00:58Z","external_id":{"arxiv":["2106.01274"]},"author":[{"last_name":"Agresti","first_name":"Antonio","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","full_name":"Agresti, Antonio"},{"full_name":"Veraar, Mark","first_name":"Mark","last_name":"Veraar"}],"title":"Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions","day":"01","_id":"15119","article_processing_charge":"No","oa_version":"Preprint","article_type":"original","scopus_import":"1","intvolume":"        60","department":[{"_id":"JuFi"}],"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","citation":{"short":"A. Agresti, M. Veraar, Annales de l’institut Henri Poincare Probability and Statistics 60 (2024) 413–430.","mla":"Agresti, Antonio, and Mark Veraar. “Stochastic Maximal Lp(Lq)-Regularity for Second Order Systems with Periodic Boundary Conditions.” <i>Annales de l’institut Henri Poincare Probability and Statistics</i>, vol. 60, no. 1, Institute of Mathematical Statistics, 2024, pp. 413–30, doi:<a href=\"https://doi.org/10.1214/22-AIHP1333\">10.1214/22-AIHP1333</a>.","ieee":"A. Agresti and M. Veraar, “Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions,” <i>Annales de l’institut Henri Poincare Probability and Statistics</i>, vol. 60, no. 1. Institute of Mathematical Statistics, pp. 413–430, 2024.","ista":"Agresti A, Veraar M. 2024. Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions. Annales de l’institut Henri Poincare Probability and Statistics. 60(1), 413–430.","chicago":"Agresti, Antonio, and Mark Veraar. “Stochastic Maximal Lp(Lq)-Regularity for Second Order Systems with Periodic Boundary Conditions.” <i>Annales de l’institut Henri Poincare Probability and Statistics</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/22-AIHP1333\">https://doi.org/10.1214/22-AIHP1333</a>.","ama":"Agresti A, Veraar M. Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions. <i>Annales de l’institut Henri Poincare Probability and Statistics</i>. 2024;60(1):413-430. doi:<a href=\"https://doi.org/10.1214/22-AIHP1333\">10.1214/22-AIHP1333</a>","apa":"Agresti, A., &#38; Veraar, M. (2024). Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions. <i>Annales de l’institut Henri Poincare Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AIHP1333\">https://doi.org/10.1214/22-AIHP1333</a>"},"issue":"1","doi":"10.1214/22-AIHP1333","page":"413-430","year":"2024","oa":1,"language":[{"iso":"eng"}],"arxiv":1,"month":"02","type":"journal_article","acknowledgement":"The first author has been partially supported by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO). The authors thank the anonymous referees and Max Sauerbrey for careful reading and helpful suggestions.","publication_identifier":{"issn":["0246-0203"]},"status":"public","volume":60},{"month":"08","arxiv":1,"isi":1,"oa":1,"year":"2024","language":[{"iso":"eng"}],"page":"4870-4927","doi":"10.1137/23M1562482","issue":"4","volume":56,"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"ec_funded":1,"status":"public","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).","type":"journal_article","project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems","author":[{"orcid":"0000-0002-9573-2962","first_name":"Antonio","last_name":"Agresti","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","full_name":"Agresti, Antonio"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}],"date_created":"2024-08-04T22:01:21Z","external_id":{"arxiv":["2301.06897"],"isi":["001315424500021"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.06897","open_access":"1"}],"date_updated":"2025-09-08T08:46:57Z","abstract":[{"lang":"eng","text":"In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the  d-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g. the Allen-Cahn equation), and dissipative systems (e.g. equations in coagulation dynamics). Moreover, we prove global well-posedness for two weakly dissipative systems: Lotka-Volterra equations for  d∈{1,2,3,4}  and the Brusselator for  d∈{1,2,3}. Many of the results are also new without transport noise. The proofs are based on maximal regularity techniques, positivity results, and sharp blow-up criteria developed in our recent works, combined with energy estimates based on Itô's formula and stochastic Gronwall inequalities. Key novelties include the introduction of new  Lζ -coercivity/dissipativity conditions and the development of an  Lp(Lq) -framework for systems of reaction-diffusion equations, which are needed when treating dimensions  d∈{2,3}  in the case of cubic or higher order nonlinearities."}],"publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication":"SIAM Journal on Mathematical Analysis","date_published":"2024-08-01T00:00:00Z","corr_author":"1","quality_controlled":"1","citation":{"chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative Systems.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/23M1562482\">https://doi.org/10.1137/23M1562482</a>.","apa":"Agresti, A., &#38; Veraar, M. (2024). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/23M1562482\">https://doi.org/10.1137/23M1562482</a>","ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems. <i>SIAM Journal on Mathematical Analysis</i>. 2024;56(4):4870-4927. doi:<a href=\"https://doi.org/10.1137/23M1562482\">10.1137/23M1562482</a>","short":"A. Agresti, M. Veraar, SIAM Journal on Mathematical Analysis 56 (2024) 4870–4927.","mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative Systems.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 56, no. 4, Society for Industrial and Applied Mathematics, 2024, pp. 4870–927, doi:<a href=\"https://doi.org/10.1137/23M1562482\">10.1137/23M1562482</a>.","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 56, no. 4. Society for Industrial and Applied Mathematics, pp. 4870–4927, 2024.","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."},"publisher":"Society for Industrial and Applied Mathematics","scopus_import":"1","article_type":"original","department":[{"_id":"JuFi"}],"intvolume":"        56","day":"01","article_processing_charge":"No","oa_version":"Preprint","_id":"17372"},{"abstract":[{"lang":"eng","text":"In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equations, where uniform trace estimates on the half-line are shown."}],"date_updated":"2023-08-16T11:41:42Z","date_created":"2023-01-29T23:00:59Z","external_id":{"arxiv":["2104.05063"],"isi":["000914134900001"]},"title":"On the trace embedding and its applications to evolution equations","author":[{"first_name":"Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"full_name":"Lindemulder, Nick","first_name":"Nick","last_name":"Lindemulder"},{"last_name":"Veraar","first_name":"Mark","full_name":"Veraar, Mark"}],"date_published":"2023-04-01T00:00:00Z","file_date_updated":"2023-08-16T11:40:02Z","publication":"Mathematische Nachrichten","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publisher":"Wiley","ddc":["510"],"citation":{"ista":"Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350.","ieee":"A. Agresti, N. Lindemulder, and M. Veraar, “On the trace embedding and its applications to evolution equations,” <i>Mathematische Nachrichten</i>, vol. 296, no. 4. Wiley, pp. 1319–1350, 2023.","mla":"Agresti, Antonio, et al. “On the Trace Embedding and Its Applications to Evolution Equations.” <i>Mathematische Nachrichten</i>, vol. 296, no. 4, Wiley, 2023, pp. 1319–50, doi:<a href=\"https://doi.org/10.1002/mana.202100192\">10.1002/mana.202100192</a>.","short":"A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023) 1319–1350.","apa":"Agresti, A., Lindemulder, N., &#38; Veraar, M. (2023). On the trace embedding and its applications to evolution equations. <i>Mathematische Nachrichten</i>. Wiley. <a href=\"https://doi.org/10.1002/mana.202100192\">https://doi.org/10.1002/mana.202100192</a>","ama":"Agresti A, Lindemulder N, Veraar M. On the trace embedding and its applications to evolution equations. <i>Mathematische Nachrichten</i>. 2023;296(4):1319-1350. doi:<a href=\"https://doi.org/10.1002/mana.202100192\">10.1002/mana.202100192</a>","chicago":"Agresti, Antonio, Nick Lindemulder, and Mark Veraar. “On the Trace Embedding and Its Applications to Evolution Equations.” <i>Mathematische Nachrichten</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/mana.202100192\">https://doi.org/10.1002/mana.202100192</a>."},"quality_controlled":"1","_id":"12429","article_processing_charge":"No","oa_version":"Published Version","day":"01","intvolume":"       296","department":[{"_id":"JuFi"}],"article_type":"original","scopus_import":"1","isi":1,"arxiv":1,"license":"https://creativecommons.org/licenses/by-nc/4.0/","month":"04","issue":"4","doi":"10.1002/mana.202100192","page":"1319-1350","has_accepted_license":"1","file":[{"file_id":"14067","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","date_created":"2023-08-16T11:40:02Z","content_type":"application/pdf","checksum":"6f099f1d064173784d1a27716a2cc795","file_size":449280,"date_updated":"2023-08-16T11:40:02Z","file_name":"2023_MathNachrichten_Agresti.pdf"}],"language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png"},"year":"2023","oa":1,"status":"public","publication_identifier":{"eissn":["1522-2616"],"issn":["0025-584X"]},"volume":296,"type":"journal_article","acknowledgement":"The first author has been partially supported by the Nachwuchsring—Network for the promotion of young scientists—at TU Kaiserslautern. The second and third authors were supported by the Vidi subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO)."},{"type":"journal_article","acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 948819) Image 1. The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","status":"public","ec_funded":1,"publication_identifier":{"eissn":["1090-2732"],"issn":["0022-0396"]},"volume":368,"issue":"9","doi":"10.1016/j.jde.2023.05.038","has_accepted_license":"1","page":"247-300","language":[{"iso":"eng"}],"file":[{"checksum":"246b703b091dfe047bfc79abf0891a63","file_size":834638,"content_type":"application/pdf","file_name":"2023_JourDifferentialEquations_Agresti.pdf","date_updated":"2024-01-29T11:03:09Z","date_created":"2024-01-29T11:03:09Z","relation":"main_file","access_level":"open_access","success":1,"creator":"dernst","file_id":"14895"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2023","oa":1,"isi":1,"month":"09","_id":"13135","oa_version":"Published Version","article_processing_charge":"Yes (in subscription journal)","day":"25","intvolume":"       368","department":[{"_id":"JuFi"}],"scopus_import":"1","article_type":"original","publisher":"Elsevier","ddc":["510"],"citation":{"mla":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” <i>Journal of Differential Equations</i>, vol. 368, no. 9, Elsevier, 2023, pp. 247–300, doi:<a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">10.1016/j.jde.2023.05.038</a>.","short":"A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.","ieee":"A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity,” <i>Journal of Differential Equations</i>, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.","ista":"Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. Journal of Differential Equations. 368(9), 247–300.","chicago":"Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.” <i>Journal of Differential Equations</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">https://doi.org/10.1016/j.jde.2023.05.038</a>.","ama":"Agresti A, Veraar M. Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. <i>Journal of Differential Equations</i>. 2023;368(9):247-300. doi:<a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">10.1016/j.jde.2023.05.038</a>","apa":"Agresti, A., &#38; Veraar, M. (2023). Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity. <i>Journal of Differential Equations</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jde.2023.05.038\">https://doi.org/10.1016/j.jde.2023.05.038</a>"},"quality_controlled":"1","corr_author":"1","date_published":"2023-09-25T00:00:00Z","publication":"Journal of Differential Equations","file_date_updated":"2024-01-29T11:03:09Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","abstract":[{"lang":"eng","text":"In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model."}],"date_updated":"2025-04-14T07:53:59Z","external_id":{"isi":["001019018700001"]},"date_created":"2023-06-18T22:00:45Z","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity","author":[{"first_name":"Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","full_name":"Agresti, Antonio"},{"first_name":"Mark","last_name":"Veraar","full_name":"Veraar, Mark"}],"project":[{"call_identifier":"H2020","name":"Bridging Scales in Random Materials","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}]},{"has_accepted_license":"1","doi":"10.1016/j.jfa.2023.110146","issue":"11","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"language":[{"iso":"eng"}],"file":[{"date_updated":"2024-01-10T11:23:57Z","file_name":"2023_JourFunctionalAnalysis_Agresti.pdf","file_size":1120592,"checksum":"eda98ca2aa73da91bd074baed34c2b3c","content_type":"application/pdf","relation":"main_file","date_created":"2024-01-10T11:23:57Z","creator":"dernst","success":1,"access_level":"open_access","file_id":"14789"}],"oa":1,"year":"2023","arxiv":1,"isi":1,"month":"12","type":"journal_article","acknowledgement":"We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for valuable discussions. We also thank the anonymous referees for their helpful comments and suggestions, and for the very accurate reading of the manuscript.\r\nThe first author has been supported partially by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. Both authors have been supported by MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative of the Federal State of Rhineland-Palatinate, Germany.","status":"public","publication_identifier":{"issn":["0022-1236"]},"keyword":["Analysis"],"volume":285,"corr_author":"1","article_number":"110146","date_published":"2023-12-01T00:00:00Z","publication":"Journal of Functional Analysis","file_date_updated":"2024-01-10T11:23:57Z","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.","lang":"eng"}],"date_updated":"2024-10-09T21:07:48Z","title":"Maximal Lp-regularity and H∞-calculus for block operator matrices and applications","author":[{"orcid":"0000-0002-9573-2962","last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"full_name":"Hussein, Amru","last_name":"Hussein","first_name":"Amru"}],"date_created":"2024-01-10T09:15:18Z","external_id":{"isi":["001081809000001"],"arxiv":["2108.01962"]},"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","_id":"14772","day":"01","department":[{"_id":"JuFi"}],"intvolume":"       285","article_type":"original","scopus_import":"1","publisher":"Elsevier","ddc":["510"],"citation":{"mla":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” <i>Journal of Functional Analysis</i>, vol. 285, no. 11, 110146, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">10.1016/j.jfa.2023.110146</a>.","short":"A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).","ieee":"A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block operator matrices and applications,” <i>Journal of Functional Analysis</i>, vol. 285, no. 11. Elsevier, 2023.","ista":"Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.","chicago":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">https://doi.org/10.1016/j.jfa.2023.110146</a>.","ama":"Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. <i>Journal of Functional Analysis</i>. 2023;285(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">10.1016/j.jfa.2023.110146</a>","apa":"Agresti, A., &#38; Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">https://doi.org/10.1016/j.jfa.2023.110146</a>"},"quality_controlled":"1"},{"license":"https://creativecommons.org/licenses/by/3.0/","month":"08","isi":1,"arxiv":1,"file":[{"relation":"main_file","date_created":"2022-08-01T10:39:36Z","file_name":"2022_Nonlinearity_Agresti.pdf","date_updated":"2022-08-01T10:39:36Z","checksum":"997a4bff2dfbee3321d081328c2f1e1a","file_size":2122096,"content_type":"application/pdf","file_id":"11715","creator":"dernst","success":1,"access_level":"open_access"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode"},"year":"2022","oa":1,"issue":"8","doi":"10.1088/1361-6544/abd613","has_accepted_license":"1","page":"4100-4210","volume":35,"status":"public","publication_identifier":{"issn":["0951-7715"],"eissn":["1361-6544"]},"acknowledgement":"The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).","type":"journal_article","date_created":"2022-07-31T22:01:47Z","external_id":{"arxiv":["2001.00512"],"isi":["000826695900001"]},"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","full_name":"Agresti, Antonio","first_name":"Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962"},{"first_name":"Mark","last_name":"Veraar","full_name":"Veraar, Mark"}],"title":"Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence","abstract":[{"text":"In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local existence and well-posedness. A second part in preparation is on blow-up criteria and regularization. Our theory is formulated in an Lp-setting, and because of this we can deal with nonlinearities in a very efficient way. Applications to several concrete problems and their quasilinear variants are given. This includes Burgers' equation, the Allen–Cahn equation, the Cahn–Hilliard equation, reaction–diffusion equations, and the porous media equation. The interplay of the nonlinearities and the critical spaces of initial data leads to new results and insights for these SPDEs. The proofs are based on recent developments in maximal regularity theory for the linearized problem for deterministic and stochastic evolution equations. In particular, our theory can be seen as a stochastic version of the theory of critical spaces due to Prüss–Simonett–Wilke (2018). Sharp weighted time-regularity allow us to deal with rough initial values and obtain instantaneous regularization results. The abstract well-posedness results are obtained by a combination of several sophisticated splitting and truncation arguments.","lang":"eng"}],"date_updated":"2023-08-03T12:25:08Z","publication":"Nonlinearity","file_date_updated":"2022-08-01T10:39:36Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","date_published":"2022-08-04T00:00:00Z","ddc":["510"],"quality_controlled":"1","citation":{"ista":"Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity. 35(8), 4100–4210.","mla":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.” <i>Nonlinearity</i>, vol. 35, no. 8, IOP Publishing, 2022, pp. 4100–210, doi:<a href=\"https://doi.org/10.1088/1361-6544/abd613\">10.1088/1361-6544/abd613</a>.","short":"A. Agresti, M. Veraar, Nonlinearity 35 (2022) 4100–4210.","ieee":"A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence,” <i>Nonlinearity</i>, vol. 35, no. 8. IOP Publishing, pp. 4100–4210, 2022.","apa":"Agresti, A., &#38; Veraar, M. (2022). Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/abd613\">https://doi.org/10.1088/1361-6544/abd613</a>","ama":"Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. <i>Nonlinearity</i>. 2022;35(8):4100-4210. doi:<a href=\"https://doi.org/10.1088/1361-6544/abd613\">10.1088/1361-6544/abd613</a>","chicago":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.” <i>Nonlinearity</i>. IOP Publishing, 2022. <a href=\"https://doi.org/10.1088/1361-6544/abd613\">https://doi.org/10.1088/1361-6544/abd613</a>."},"publisher":"IOP Publishing","intvolume":"        35","department":[{"_id":"JuFi"}],"article_type":"original","scopus_import":"1","_id":"11701","article_processing_charge":"No","oa_version":"Published Version","day":"04"},{"intvolume":"        22","department":[{"_id":"JuFi"}],"article_type":"original","scopus_import":"1","_id":"11858","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","day":"01","ddc":["510"],"citation":{"chicago":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” <i>Journal of Evolution Equations</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00028-022-00786-7\">https://doi.org/10.1007/s00028-022-00786-7</a>.","ama":"Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in critical spaces part II. <i>Journal of Evolution Equations</i>. 2022;22(2). doi:<a href=\"https://doi.org/10.1007/s00028-022-00786-7\">10.1007/s00028-022-00786-7</a>","apa":"Agresti, A., &#38; Veraar, M. (2022). Nonlinear parabolic stochastic evolution equations in critical spaces part II. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00786-7\">https://doi.org/10.1007/s00028-022-00786-7</a>","short":"A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).","mla":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” <i>Journal of Evolution Equations</i>, vol. 22, no. 2, 56, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s00028-022-00786-7\">10.1007/s00028-022-00786-7</a>.","ieee":"A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations in critical spaces part II,” <i>Journal of Evolution Equations</i>, vol. 22, no. 2. Springer Nature, 2022.","ista":"Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 22(2), 56."},"quality_controlled":"1","publisher":"Springer Nature","publication":"Journal of Evolution Equations","file_date_updated":"2022-08-16T08:52:46Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","article_number":"56","corr_author":"1","date_published":"2022-06-01T00:00:00Z","external_id":{"isi":["000809108500001"]},"date_created":"2022-08-16T08:39:43Z","author":[{"orcid":"0000-0002-9573-2962","last_name":"Agresti","first_name":"Antonio","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"first_name":"Mark","last_name":"Veraar","full_name":"Veraar, Mark"}],"title":"Nonlinear parabolic stochastic evolution equations in critical spaces part II","abstract":[{"text":"This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical spaces. In the first main result we obtain several new blow-up criteria for quasi- and semilinear stochastic evolution equations. In particular, for semilinear equations we obtain a Serrin type blow-up criterium, which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074, 2018) to the stochastic setting. Blow-up criteria can be used to prove global well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights in time play a central role in the proofs. Our second contribution is a new method to bootstrap Sobolev and Hölder regularity in time and space, which does not require smoothness of the initial data. The blow-up criteria are at the basis of these new methods. Moreover, in applications the bootstrap results can be combined with our blow-up criteria, to obtain efficient ways to prove global existence. This gives new results even in classical 𝐿2-settings, which we illustrate for a concrete SPDE. In future works in preparation we apply the results of the current paper to obtain global well-posedness results and regularity for several concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into a more flexible framework, where less restrictions on the nonlinearities are needed, and we are able to treat rough initial values from critical spaces. Moreover, we will obtain higher-order regularity results.","lang":"eng"}],"date_updated":"2024-10-09T21:03:06Z","acknowledgement":"The authors thank Emiel Lorist for helpful comments. The authors thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","type":"journal_article","keyword":["Mathematics (miscellaneous)"],"volume":22,"status":"public","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"language":[{"iso":"eng"}],"file":[{"creator":"kschuh","success":1,"access_level":"open_access","file_id":"11862","file_name":"2022_Journal of Evolution Equations_Agresti.pdf","date_updated":"2022-08-16T08:52:46Z","content_type":"application/pdf","file_size":1758371,"checksum":"59b99d1b48b6bd40983e7ce298524a21","relation":"main_file","date_created":"2022-08-16T08:52:46Z"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","oa":1,"doi":"10.1007/s00028-022-00786-7","issue":"2","has_accepted_license":"1","month":"06","isi":1}]