Stochastic Two-Dimensional Anisotropic Magnetohydrodynamics System with Multiplicative Noise

Abstract: In this paper, we investigate the stochastic two-dimensional anisotropic magnetohydrodynamics system on $\mathbb T<sup>2$ with velocity dissipation acting only in the horizontal direction. Under multiplicative noise, we prove the existence of global martingale solutions and global probabilistically weak solutions, together with pathwise uniqueness.