Weak solutions to the equations of motion for compressible magnetic fluids

Abstract

We study the differential system governing the flow of a compressible magnetic fluid under the action of a magnetic field. The system is a combination of the compressible Navier–Stokes equations, the angular momentum equation, the magnetization equation and the magnetostatic equations. We prove global-in-time existence of weak solutions with finite energy to the system posed in a bounded domain of R 3 and equipped with initial and boundary conditions.