Global classical solutions to an evolutionary model for magnetoelasticity
Analysis of PDEs
2019-04-23 v1
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 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 , 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.
Cite
@article{arxiv.1904.09531,
title = {Global classical solutions to an evolutionary model for magnetoelasticity},
author = {Ning Jiang and Hui Liu and Yi-Long Luo},
journal= {arXiv preprint arXiv:1904.09531},
year = {2019}
}
Comments
34 pages, any comment wellcome