Global solvability of the Rosensweig system for ferrofluids in bounded domains

Abstract

We consider the partial differential equations proposed by Rosensweig to model the dynamics of an incompressible viscous ferrofluid under the action of an external magnetic field. The Rosensweig system consists of the Navier–Stokes equations, the angular momentum equations, the magnetization equations and the magnetostatic equations. The magnetization equations are of Bloch type, and no regularizing term is added. We prove the global existence of unique strong solution to the initial boundary value problem for the system in a bounded domain, with the initial data and external magnetic field around constant magnetic fields.