Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise

Abstract

We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system that is forced by random noise of an additive and a linear multiplicative type and has viscous and magnetic diffusion, both of which are weaker than a full Laplacian. We apply convex integration to both equations of velocity and magnetic fields in order to obtain the non-uniqueness in law in the class of probabilistically strong solutions.