Reflection of Stochastic Evolution Equations in Infinite Dimensional Domains

TL;DR

This paper proves the existence and uniqueness of solutions for stochastic evolution equations with reflection in infinite-dimensional spaces, applicable to models like stochastic Navier-Stokes equations.

Contribution

It introduces a general framework for reflecting stochastic evolution equations in infinite dimensions, extending previous results to broader classes of equations.

Findings

Existence of solutions established

Uniqueness of solutions proven

Framework applicable to stochastic Navier-Stokes equations

Abstract

In this paper, we establish the existence and the uniqueness of solutions of stochastic evolution equations (SEEs) with reflection in an infinite dimensional ball. Our framework is sufficiently general to include e.g. the stochastic Navier-Stokes equations.