Well-posedness for the ferromagnetic MHD equation

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 talk, we will discuss some of the physics that led to the development of these equations and the mathematical simplifications we make based on physical principles. Moreover, we will give an overview of the proof for the local-in-time existence of solutions, their uniqueness and regularity as well.