Stochastic 2D Navier-Stokes equations on time-dependent domains

TL;DR

This paper proves the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations on moving domains, using domain transformations, Galerkin approximations, and probabilistic methods.

Contribution

It introduces a novel approach to handle stochastic Navier-Stokes equations on time-dependent domains, establishing well-posedness through domain transformation and advanced stochastic analysis.

Findings

Existence of martingale solutions on moving domains

Pathwise uniqueness of solutions established

Solutions constructed via Galerkin approximations

Abstract

We establish the existence and uniqueness of solutions to stochastic 2D Navier-Stokes equations in a time-dependent domain driven by Brownian motion. A martingale solution is constructed through domain transformation and appropriate Galerkin approximations on time-dependent spaces. The probabilistic strong solution follows from the pathwise uniqueness and the Yamada-Watanable theorem.