On well-posedness of an evolutionary model for magnetoelasticity: hydrodynamics of viscoelasticity and Landau-Lifshitz-Gilbert systems

Abstract

In this paper, we first prove the local-in-time existence of the evolutionary model for magnetoelasticity with finite initial energy by employing the nonlinear iterative approach to deal with the constraint on values of the magnetization |M(t,x)|=1 in the Landau-Lifshitz-Gilbert (LLG) equation. We reformulate the evolutionary model near the constant equilibrium for magnetoelasticity with vanishing external magnetic field, so that a further dissipative term will be sought from the elastic stress. We thereby justify the global well-posedness to the evolutionary model for magnetoelasticity with zero external magnetic field under small size of initial data.