Global classical solutions to an evolutionary model for magnetoelasticity

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 given in \cite{Jiang-Luo-2019-SIAM} to deal with the geometric constraint $M\in {\mathbb{S}}^{d-1}$ in the Landau-Lifshitz-Gilbert (LLG) equation. Inspired by \cite{Lin-Liu-Zhang-CPAM2005, Lin-Zhang-2008-CPAM}, we reformulate the evolutionary model for magnetoelasticity with vanishing external magnetic field $H_{ext}$, 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.

arXiv comment34 pages, any comment wellcome

References in corpus (2)

• Existence results for incompressible magnetoelasticity
• A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis

Cited by in corpus (1)

• Smooth solutions to the Schrödinger flow for maps from smooth bounded domains in Euclidean spaces into ${\mathbb{S}}^2$