Global Weak Solutions to Magnetic Fluid Flows with Nonlinear Maxwell–Cattaneo Heat Transfer Law

Abstract

We discuss the equations describing the dynamic of the heat transfer in a magnetic fluid flow under the action of an applied magnetic field. Instead of the usual heat transfer equation we use a generalization given by the Maxwell–Cattaneo law which is a system satisfied by the temperature and the heat flux. We prove a global existence of weak solutions to the system having a finite energy.