Dissipative measure valued solutions to the stochastic compressible Navier–Stokes equations and inviscid–incompressible limit

We introduce the concept of dissipative measure-valued martingale solutions for the stochastic compressible Navier–Stokes equations. These solutions are probabilistically weak, as they incorporate both the underlying Wiener process and the probability space as intrinsic components of the formulation. For the stochastic compressible Navier–Stokes system, we further derive a relative energy inequality, which serves as the foundation for establishing a 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.