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

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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, the local-in-time existence of the evolutionary model for magnetoelasticity with finite initial energy is proven by using the nonlinear iterative approach to handle the constraint on values of the magnetization |M(t, x)| = 1 in the Landau-Lifshitz-Gilbert (LLG) equation. The evolutionary model for magnetoelasticity with zero external magnetic field is reformulated near the constant equilibrium, and a dissipative term is introduced from the elastic stress. The global well-posedness of the model is justified under small size of initial data.(c) 2023 Elsevier Inc. All rights reserved.