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

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.