[{"has_accepted_license":"1","department":[{"_id":"JuFi"}],"date_created":"2024-01-10T09:15:18Z","file":[{"success":1,"file_id":"14789","creator":"dernst","relation":"main_file","content_type":"application/pdf","checksum":"eda98ca2aa73da91bd074baed34c2b3c","date_created":"2024-01-10T11:23:57Z","file_size":1120592,"file_name":"2023_JourFunctionalAnalysis_Agresti.pdf","access_level":"open_access","date_updated":"2024-01-10T11:23:57Z"}],"month":"12","article_type":"original","date_published":"2023-12-01T00:00:00Z","scopus_import":"1","publisher":"Elsevier","language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis","issue":"11","file_date_updated":"2024-01-10T11:23:57Z","day":"01","type":"journal_article","intvolume":"       285","status":"public","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"110146","isi":1,"ddc":["510"],"doi":"10.1016/j.jfa.2023.110146","year":"2023","title":"Maximal Lp-regularity and H∞-calculus for block operator matrices and applications","external_id":{"arxiv":["2108.01962"],"isi":["001081809000001"]},"arxiv":1,"article_processing_charge":"Yes (in subscription journal)","oa":1,"volume":285,"date_updated":"2024-01-10T11:24:56Z","publication_identifier":{"issn":["0022-1236"]},"_id":"14772","oa_version":"Published Version","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","citation":{"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.","short":"A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).","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>","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>.","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>.","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>","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."},"publication_status":"published","abstract":[{"lang":"eng","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."}],"author":[{"first_name":"Antonio","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","last_name":"Agresti","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Hussein","full_name":"Hussein, Amru","first_name":"Amru"}],"keyword":["Analysis"]},{"doi":"10.1016/j.jde.2023.05.038","year":"2023","ec_funded":1,"title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity","external_id":{"isi":["001019018700001"]},"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"ddc":["510"],"publication_status":"published","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>.","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>","short":"A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.","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.","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>","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.","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>."},"abstract":[{"text":"In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity estimates and sharp blow-up criteria. We view the results of this paper as a general toolbox for establishing global well-posedness for a large class of reaction-diffusion systems of practical interest, of which many are completely open. In our follow-up work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra equations and the Brusselator model.","lang":"eng"}],"author":[{"first_name":"Antonio","full_name":"Agresti, Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Veraar","full_name":"Veraar, Mark","first_name":"Mark"}],"oa":1,"date_updated":"2024-01-29T11:04:41Z","volume":368,"article_processing_charge":"Yes (in subscription journal)","_id":"13135","publication_identifier":{"issn":["0022-0396"],"eissn":["1090-2732"]},"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).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","quality_controlled":"1","project":[{"call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","grant_number":"948819"}],"month":"09","article_type":"original","date_published":"2023-09-25T00:00:00Z","publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"JuFi"}],"file":[{"success":1,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"14895","file_name":"2023_JourDifferentialEquations_Agresti.pdf","file_size":834638,"date_created":"2024-01-29T11:03:09Z","checksum":"246b703b091dfe047bfc79abf0891a63","date_updated":"2024-01-29T11:03:09Z","access_level":"open_access"}],"date_created":"2023-06-18T22:00:45Z","day":"25","type":"journal_article","intvolume":"       368","status":"public","issue":"9","publication":"Journal of Differential Equations","file_date_updated":"2024-01-29T11:03:09Z","page":"247-300"},{"language":[{"iso":"eng"}],"publisher":"Wiley","scopus_import":"1","article_type":"original","date_published":"2023-04-01T00:00:00Z","month":"04","file":[{"success":1,"relation":"main_file","content_type":"application/pdf","file_id":"14067","creator":"dernst","file_size":449280,"file_name":"2023_MathNachrichten_Agresti.pdf","checksum":"6f099f1d064173784d1a27716a2cc795","date_created":"2023-08-16T11:40:02Z","access_level":"open_access","date_updated":"2023-08-16T11:40:02Z"}],"date_created":"2023-01-29T23:00:59Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","status":"public","intvolume":"       296","type":"journal_article","day":"01","page":"1319-1350","file_date_updated":"2023-08-16T11:40:02Z","issue":"4","publication":"Mathematische Nachrichten","external_id":{"isi":["000914134900001"],"arxiv":["2104.05063"]},"title":"On the trace embedding and its applications to evolution equations","doi":"10.1002/mana.202100192","year":"2023","ddc":["510"],"isi":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)"},"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","first_name":"Antonio"},{"first_name":"Nick","full_name":"Lindemulder, Nick","last_name":"Lindemulder"},{"first_name":"Mark","full_name":"Veraar, Mark","last_name":"Veraar"}],"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."}],"publication_status":"published","citation":{"short":"A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023) 1319–1350.","ista":"Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350.","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>.","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>.","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>","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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).","oa_version":"Published Version","quality_controlled":"1","_id":"12429","publication_identifier":{"issn":["0025-584X"],"eissn":["1522-2616"]},"volume":296,"date_updated":"2023-08-16T11:41:42Z","oa":1,"article_processing_charge":"No","arxiv":1},{"ddc":["510"],"main_file_link":[{"url":"https://doi.org/10.1007/s40072-023-00319-4","open_access":"1"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"external_id":{"arxiv":["2207.08293"]},"title":"Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations","ec_funded":1,"year":"2023","doi":"10.1007/s40072-023-00319-4","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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. ","oa_version":"Submitted Version","project":[{"grant_number":"948819","call_identifier":"H2020","name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d"}],"_id":"12486","publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"oa":1,"date_updated":"2023-12-18T07:53:45Z","article_processing_charge":"No","arxiv":1,"author":[{"orcid":"0000-0002-9573-2962","last_name":"Agresti","full_name":"Agresti, Antonio","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"}],"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."}],"publication_status":"epub_ahead","citation":{"short":"A. Agresti, Stochastics and Partial Differential Equations: Analysis and Computations (2023).","ista":"Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations. Stochastics and Partial Differential Equations: Analysis and Computations.","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>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s40072-023-00319-4\">10.1007/s40072-023-00319-4</a>.","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>. 2023. doi:<a href=\"https://doi.org/10.1007/s40072-023-00319-4\">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, 2023. <a href=\"https://doi.org/10.1007/s40072-023-00319-4\">https://doi.org/10.1007/s40072-023-00319-4</a>.","apa":"Agresti, A. (2023). 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>","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>. Springer Nature, 2023."},"date_created":"2023-02-02T10:45:47Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","article_type":"original","date_published":"2023-11-28T00:00:00Z","month":"11","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","status":"public","type":"journal_article","day":"28"},{"file_date_updated":"2022-08-01T10:39:36Z","page":"4100-4210","issue":"8","publication":"Nonlinearity","type":"journal_article","day":"04","status":"public","intvolume":"        35","department":[{"_id":"JuFi"}],"has_accepted_license":"1","date_created":"2022-07-31T22:01:47Z","file":[{"file_name":"2022_Nonlinearity_Agresti.pdf","file_size":2122096,"date_created":"2022-08-01T10:39:36Z","checksum":"997a4bff2dfbee3321d081328c2f1e1a","date_updated":"2022-08-01T10:39:36Z","access_level":"open_access","success":1,"content_type":"application/pdf","relation":"main_file","file_id":"11715","creator":"dernst"}],"article_type":"original","date_published":"2022-08-04T00:00:00Z","month":"08","language":[{"iso":"eng"}],"publisher":"IOP Publishing","scopus_import":"1","oa":1,"volume":35,"date_updated":"2023-08-03T12:25:08Z","article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO).","oa_version":"Published Version","quality_controlled":"1","_id":"11701","publication_identifier":{"issn":["0951-7715"],"eissn":["1361-6544"]},"publication_status":"published","citation":{"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>","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>.","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.","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>","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>."},"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","last_name":"Agresti","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","first_name":"Antonio"},{"first_name":"Mark","full_name":"Veraar, Mark","last_name":"Veraar"}],"abstract":[{"lang":"eng","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."}],"isi":1,"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"},"ddc":["510"],"year":"2022","doi":"10.1088/1361-6544/abd613","title":"Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence","external_id":{"arxiv":["2001.00512"],"isi":["000826695900001"]}},{"has_accepted_license":"1","department":[{"_id":"JuFi"}],"date_created":"2022-08-16T08:39:43Z","file":[{"relation":"main_file","content_type":"application/pdf","creator":"kschuh","file_id":"11862","success":1,"access_level":"open_access","date_updated":"2022-08-16T08:52:46Z","file_size":1758371,"file_name":"2022_Journal of Evolution Equations_Agresti.pdf","checksum":"59b99d1b48b6bd40983e7ce298524a21","date_created":"2022-08-16T08:52:46Z"}],"month":"06","article_type":"original","date_published":"2022-06-01T00:00:00Z","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"publication":"Journal of Evolution Equations","issue":"2","file_date_updated":"2022-08-16T08:52:46Z","day":"01","type":"journal_article","intvolume":"        22","status":"public","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"56","isi":1,"ddc":["510"],"year":"2022","doi":"10.1007/s00028-022-00786-7","title":"Nonlinear parabolic stochastic evolution equations in critical spaces part II","external_id":{"isi":["000809108500001"]},"article_processing_charge":"Yes (via OA deal)","oa":1,"volume":22,"date_updated":"2023-08-03T12:53:51Z","publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"_id":"11858","quality_controlled":"1","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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).","citation":{"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>.","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>","short":"A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).","ista":"Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 22(2), 56.","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>","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.","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>."},"publication_status":"published","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"}],"keyword":["Mathematics (miscellaneous)"],"author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","first_name":"Antonio","orcid":"0000-0002-9573-2962","last_name":"Agresti","full_name":"Agresti, Antonio"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}]},{"month":"10","date_published":"2022-10-27T00:00:00Z","article_type":"original","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"department":[{"_id":"JuFi"}],"date_created":"2023-01-12T12:12:29Z","day":"27","type":"journal_article","status":"public","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","doi":"10.1007/s40072-022-00277-3","year":"2022","external_id":{"isi":["000874389000001"]},"title":"The stochastic primitive equations with transport noise and turbulent pressure","isi":1,"main_file_link":[{"url":"https://doi.org/10.1007/s40072-022-00277-3","open_access":"1"}],"citation":{"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>. Springer Nature, 2022.","apa":"Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2022). 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>","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, 2022. <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>. 2022. doi:<a href=\"https://doi.org/10.1007/s40072-022-00277-3\">10.1007/s40072-022-00277-3</a>","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>, Springer Nature, 2022, 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 (2022).","ista":"Agresti A, Hieber M, Hussein A, Saal M. 2022. The stochastic primitive equations with transport noise and turbulent pressure. Stochastics and Partial Differential Equations: Analysis and Computations."},"publication_status":"epub_ahead","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"}],"author":[{"last_name":"Agresti","full_name":"Agresti, Antonio","orcid":"0000-0002-9573-2962","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"first_name":"Matthias","last_name":"Hieber","full_name":"Hieber, Matthias"},{"last_name":"Hussein","full_name":"Hussein, Amru","first_name":"Amru"},{"first_name":"Martin","full_name":"Saal, Martin","last_name":"Saal"}],"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"article_processing_charge":"Yes (via OA deal)","date_updated":"2023-08-16T09:11:38Z","oa":1,"publication_identifier":{"issn":["2194-0401"],"eissn":["2194-041X"]},"_id":"12178","quality_controlled":"1","oa_version":"Published Version","acknowledgement":"The authors thank the anonymous referees for their helpful comments and suggestions. Open Access funding enabled and organized by Projekt DEAL.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]