@article{13135,
  abstract     = {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.},
  author       = {Agresti, Antonio and Veraar, Mark},
  issn         = {1090-2732},
  journal      = {Journal of Differential Equations},
  number       = {9},
  pages        = {247--300},
  publisher    = {Elsevier},
  title        = {{Reaction-diffusion equations with transport noise and critical superlinear diffusion: Local well-posedness and positivity}},
  doi          = {10.1016/j.jde.2023.05.038},
  volume       = {368},
  year         = {2023},
}