Well-Posedness for a Magnetohydrodynamical Model with Intrinsic Magnetisation

Abstract

Ferromagnetic magnetohydrodynamics concerns the study of conducting fluids with intrinsic magnetisation under the influence of a magnetic field. It is a generalisation of the magnetohydrodynamical equations and takes into account the dynamics of the magnetisation of a fluid. First proposed by Lingam (Lingam, `Dissipative effects in magnetohydrodynamical models with intrinsic magnetisation', Communications in Nonlinear Science and Numerical Simulation Vol 28, pp 223-231, 2015), the usual equations of magnetohydrodynamics, namely the Navier-Stokes equation and the induction equation, are coupled with the Landau-Lifshitz-Gilbert equation. In this paper, the local existence, uniqueness and regularity of weak solutions to this system are discussed.