Martingale solutions for the compressible MHD systems with stochastic external forces

TL;DR

This paper establishes the existence of martingale solutions for the three-dimensional compressible magnetohydrodynamics system under stochastic external forces, using advanced probabilistic and analytical methods.

Contribution

It introduces a novel approach to prove the existence of weak solutions for stochastic compressible MHD systems with a rigorous mathematical framework.

Findings

Existence of martingale solutions for the stochastic compressible MHD system.

Application of Galerkin approximation, stopping time, and Skorokhod theorem in the proof.

Framework for future analysis of stochastic MHD models.

Abstract

In this paper we consider the three-dimensional compressible MHD system with stochastic external forces in a bounded domain. We obtain the existence of martingale solution which is a weak solution for the fluid variables, the Brownian motion on a probability space. The construction of the solution is based on the Galerkin approximation method, stopping time, the compactness method and Jakubowski Skorokhod theorem, etc.