Stochastic MHD equations with fractional kinematic dissipation and partial magnetic diffusion in [formula omitted

Abstract

This paper focuses on a system of the 2-D MHD equations with fractional kinematic dissipation and partial magnetic diffusion under random perturbations. We first establish the local existence, uniqueness and blow-up criterion of pathwise classical solution to the corresponding SPDE with general multiplicative noise in R2. Moreover, when the noise is non-autonomous and linear, we further establish global existence and large-time behavior of pathwise solutions by exploiting the structure of the equations and some estimates on Girsanov type stochastic processes.