On signed measure valued solutions of stochastic evolution equations

TL;DR

This paper investigates the existence, uniqueness, and mass conservation of signed measure solutions for a class of stochastic evolution equations driven by Wiener sheets, including stochastic 2D Navier-Stokes equations in vorticity form.

Contribution

It introduces a framework for signed measure solutions to stochastic evolution equations, covering important cases like stochastic 2D Navier-Stokes equations.

Findings

Established existence and uniqueness of solutions.

Proved mass conservation properties.

Applied results to stochastic Navier-Stokes equations.

Abstract

We study existence, uniqueness and mass conservation of signed measure valued solutions of a class of stochastic evolution equations with respect to the Wiener sheet, including as particular cases the stochastic versions of the regularized two-dimensional Navier-Stokes equations in vorticity form introduced by Kotelenez.