Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity Agresti, Antonio ; https://orcid.org/0000-0002-9573-2962 Veraar, Mark ddc:510 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. Elsevier 2023 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/13135 https://research-explorer.ista.ac.at/download/13135/14895 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jde.2023.05.038 info:eu-repo/semantics/altIdentifier/issn/0022-0396 info:eu-repo/semantics/altIdentifier/e-issn/1090-2732 info:eu-repo/semantics/altIdentifier/wos/001019018700001 info:eu-repo/semantics/openAccess