Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit

TL;DR

This paper introduces a new class of solutions for stochastic compressible Navier-Stokes equations, establishes key inequalities, and explores the inviscid-incompressible limit, advancing understanding of stochastic fluid dynamics.

Contribution

It defines dissipative measure valued martingale solutions and proves weak-strong uniqueness and inviscid-incompressible limit results for stochastic compressible fluids.

Findings

Established relative energy inequality for the system

Proved path-wise weak-strong uniqueness principle

Analyzed inviscid-incompressible limit using energy methods

Abstract

We introduce a concept of dissipative measure valued martingale solutions for stochastic compressible Navier-Stokes equations. These solutions are weak from a probabilistic perspective, since they include both the driving Wiener process and the probability space as an integral part of the solution. Then, for the stochastic compressible Navier-Stokes system, we establish the relative energy inequality, and as a result, we demonstrate the path-wise weak-strong uniqueness principle. We also look at the inviscid-incompressible limit of the underlying system of equations using the relative energy inequality.