On the existence, uniqueness and regularity of strong solutions to a stochastic 2D Cahn–Hilliard-Magnetohydrodynamic model

We investigate a stochastic coupled model of the Cahn–Hilliard equations and the stochastic magnetohydrodynamic equations in a bounded domain of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℝ</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> {R²} . The model describes the flow of the mixture of two incompressible and immiscible fluids under the influence of an electromagnetic field with stochastic perturbations. We prove the existence, uniqueness and regularity of a probabilistic strong solution. The proof of the existence is based on the Galerkin approximation, the stopping time technique and some weak convergence principles in functional analysis.