The critical variational setting for stochastic evolution equations

A Agresti, M Veraar - Probability Theory and Related Fields, 2024 - Springer
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 …

Nonlinear parabolic stochastic evolution equations in critical spaces part II: Blow-up criteria and instantaneous regularization

A Agresti, M Veraar - Journal of Evolution Equations, 2022 - Springer
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 …

[HTML][HTML] Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity

A Agresti, M Veraar - Journal of Differential Equations, 2023 - Elsevier
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 …

Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence

A Agresti, M Veraar - Nonlinearity, 2022 - iopscience.iop.org
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 …

Nonlinear parabolic stochastic evolution equations in critical spaces Part II. Blow-up criteria and instantaneous regularization

A Agresti, M Veraar - arXiv preprint arXiv:2012.04448, 2020 - arxiv.org
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 …