The exponential behavior of a stochastic globally modified Cahn-Hilliard-Magnetohydrodynamic model with multi- plicative noise

Abstract

In this work, we explore the stability of weak solutions to a stochastic version of a globally modified coupled Cahn-Hilliard-Magnetohydrodynamic model with multiplicative noise. The model describes the flow of the mixture of two incompressible, immiscible fluids under the influence of an electomagnetic field with stochastic pertubations. This system consists of the globally modified Magnetohydrodynamic model for the velocity and magnetic field, coupled with a Cahn-Hilliard equation for the order (phase) parameter. We prove that the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions.
We also show a result related to the stabilization of these equations.