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

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.