Martingale solutions of the stochastic Hall-magnetohydrodynamics equations on $\mathbb{R}^3$

Abstract

We prove the existence of a global martingale solution of a stochastic Hall-magnetohydrodynamics equations on $\mathbb{R}^3$ with multiplicative noise. Using the Fourier analysis we construct a sequence of approximate solutions. The existence of a solution is proved via the stochastic compactness method and the Jakubowski generalization of the Skorokhod theorem for nonmetric spaces, in particular, the spaces with weak topologies. The main difficulty is caused by the Hall term which makes the equations strongly nonlinear.