Non Monotone Stochastic Evolution Equations

TL;DR

This paper introduces a generalized approach to stochastic evolution equations that accommodates nonlinear, non-monotone operators, enabling the analysis of complex problems like stochastic Navier-Stokes equations in lower dimensions.

Contribution

It extends existing embedding theorems to include non-monotone operators, facilitating the study of stochastic evolution equations with broader applicability.

Findings

Established existence of strong solutions for stochastic Navier-Stokes equations in dimension less than four.

Generalized embedding theorems applicable to nonlinear, non-monotone operators.

Demonstrated the approach's effectiveness for complex stochastic PDEs.

Abstract

An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the existence of strong solutions to a stochastic Navier Stokes problem in dimension less than four.