Existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations

Abstract

In this paper, we study a system of nonlinear stochastic partial differential equations describing the motion of turbulent non-Newtonian media in the presence of fluctuating magnetic field. The system is basically obtained by a coupling of the dynamical equations of a non-Newtonian fluids having p-structure and the Maxwell equations. We mainly show the existence of weak martingale solutions and their exponential decay when time goes to infinity.