Existence of a martingale solution of the stochastic Hall-MHD equations perturbed by Poisson type random forces on ${\mathbb{R}}^{3}$

TL;DR

This paper proves the existence of a global martingale solution for stochastic Hall-MHD equations on three-dimensional space with Poisson random forces, using advanced probabilistic and analytical methods.

Contribution

It establishes the existence of solutions for stochastic Hall-MHD equations with Poisson noise, employing Fourier truncation, stochastic compactness, and a specialized Skorokhod theorem.

Findings

Existence of a global martingale solution is proven.

Solution construction uses Fourier truncation and stochastic compactness.

Applicable to stochastic Hall-MHD equations with Poisson noise.

Abstract

Stochastic Hall-magnetohydrodynamics equations on ${\mathbb{R}}^{3}$ with random forces expressed in terms of the time homogeneous Poisson random measures are considered. We prove the existence of a global martingale solution. The construction of a solution is based on the Fourier truncation method, stochastic compactness method and a version of the Skorokhod theorem for non-metric spaces adequate for Poisson type random fields.