Compressible Euler equations with transport noise

TL;DR

This paper investigates the stochastic compressible Euler equations with transport noise, demonstrating existence, uniqueness, and regularising effects, which are relevant for turbulence modeling and mathematical fluid dynamics.

Contribution

It establishes the existence of measure-valued solutions, weak-strong uniqueness, and Markov selections for the stochastic Euler equations with transport noise, advancing the mathematical understanding of such systems.

Findings

Existence of dissipative measure-valued martingale solutions

Weak-strong uniqueness property proven

Existence of Markov selections established

Abstract

We study the isentropic compressible Euler equations in multi-dimensions with stochastic perturbation of transport type. On the one hand, this is motivated by the physical modelling in turbulence theory. On the other hand, it has been shown recently that this type of noise can have regularising effects. In this paper, we prove the existence of dissipative measure-valued martingale solutions, the weak-strong uniqueness property and the existence of Markov selections.