Local-in-time well-posedness for a magnetohydrodynamical model with intrinsic magnetisation

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 (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-in-time existence, uniqueness and regularity of strong solutions to this system are discussed.