Stochastic compressible Euler equations and inviscid limits

TL;DR

This paper establishes the existence of unique local strong solutions to the stochastic compressible Euler equations with multiplicative noise and demonstrates convergence of stochastic Navier-Stokes solutions to Euler equations as viscosity vanishes.

Contribution

It proves the existence of strong solutions for stochastic compressible Euler equations and shows the inviscid limit from stochastic Navier-Stokes to Euler equations.

Findings

Existence of unique local strong solutions to stochastic Euler equations.

Convergence of stochastic Navier-Stokes solutions to Euler equations as viscosity approaches zero.

Solutions are strong in both PDE and probabilistic senses.

Abstract

We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic sense. Based on this existence result, we study the inviscid limit of the stochastic compressible Navier--Stokes system. As the viscosity tends to zero, any sequence of finite energy weak martingale solutions converges to the compressible Euler system.