Sequential stability of weak martingale solutions to stochastic compressible Navier-Stokes equations with viscosity vanishing on vacuum

TL;DR

This paper studies the stability of weak solutions to stochastic compressible Navier-Stokes equations with vanishing viscosity on vacuum, proving sequential compactness in a 3D periodic setting.

Contribution

It establishes the sequential stability of weak martingale solutions for stochastic compressible Navier-Stokes equations with degenerate viscosity.

Findings

Weak martingale solutions are sequentially compact.

Stability holds under density-dependent viscosity with stochastic noise.

Results apply to three-dimensional periodic domains.

Abstract

In this paper, we investigate the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient driven by multiplicative stochastic noise. We consider three-dimensional periodic domain and prove that the family of weak martingale solutions is sequentially compact.