Suitable Weak Solutions of the Incompressible Magnetohydrodynamic Equations in Time Varying Domains

Abstract

The purpose of this paper is to study the three-dimensional system of magnetohydrodynamic (MHD equations) for a viscous incompressible resistive fluid. We are interested in the existence of suitable weak solutions to the system in time varying domains. To do this, we consider the approximate equations related to the MHD equations and we apply the Leray-Schauder fixed point theorem to the solutions of the equations over the moving boundary domains. Existence of suitable weak solutions is established by the energy estimates and the compactness results in Lebesgue and Sobolev spaces.