{"publisher":"Society for Industrial and Applied Mathematics","type":"journal_article","corr_author":"1","intvolume":"        56","doi":"10.1137/23M1562482","page":"4870-4927","oa":1,"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).","abstract":[{"text":"In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the  d-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g. the Allen-Cahn equation), and dissipative systems (e.g. equations in coagulation dynamics). Moreover, we prove global well-posedness for two weakly dissipative systems: Lotka-Volterra equations for  d∈{1,2,3,4}  and the Brusselator for  d∈{1,2,3}. Many of the results are also new without transport noise. The proofs are based on maximal regularity techniques, positivity results, and sharp blow-up criteria developed in our recent works, combined with energy estimates based on Itô's formula and stochastic Gronwall inequalities. Key novelties include the introduction of new  Lζ -coercivity/dissipativity conditions and the development of an  Lp(Lq) -framework for systems of reaction-diffusion equations, which are needed when treating dimensions  d∈{2,3}  in the case of cubic or higher order nonlinearities.","lang":"eng"}],"publication_status":"published","year":"2024","issue":"4","date_created":"2024-08-04T22:01:21Z","language":[{"iso":"eng"}],"publication":"SIAM Journal on Mathematical Analysis","article_processing_charge":"No","date_published":"2024-08-01T00:00:00Z","ec_funded":1,"quality_controlled":"1","article_type":"original","title":"Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.06897"}],"oa_version":"Preprint","project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"status":"public","_id":"17372","author":[{"last_name":"Agresti","first_name":"Antonio","orcid":"0000-0002-9573-2962","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"last_name":"Veraar","first_name":"Mark","full_name":"Veraar, Mark"}],"volume":56,"scopus_import":"1","month":"08","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"external_id":{"arxiv":["2301.06897"]},"day":"01","citation":{"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.","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>.","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.","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>","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>","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>."},"date_updated":"2024-08-05T08:13:13Z","department":[{"_id":"JuFi"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}