Global Weak Solutions to Equations of Motion for Magnetic Fluids

Abstract.

We study the differential system governing the flow of an incompressible ferrofluid under the action of a magnetic field. The system consists of the Navier–Stokes equations, the angular momentum equation, the magnetization equation, and the magnetostatic equations. We prove, by using the Galerkin method, a global in time existence of weak solutions with finite energy of an initial boundary-value problem and establish the long-time behavior of such solutions. The main difficulty is due to the singularity of the gradient magnetic force.