Existence of weak solutions to an evolutionary model for magnetoelasticity
Analysis of PDEs
2016-08-11 v1 Materials Science
Abstract
We prove existence of weak solutions to an evolutionary model derived for magnetoelastic materials. The model is phrased in Eulerian coordinates and consists in particular of (i) a Navier-Stokes equation that involves magnetic and elastic terms in the stress tensor obtained by a variational approach, of (ii) a regularized transport equation for the deformation gradient and of (iii) the Landau-Lifshitz-Gilbert equation for the dynamics of the magnetization. The proof is built on a Galerkin method and a fixed-point argument. It is based on ideas from F.-H. Lin and the third author for systems modeling the flow of liquid crystals as well as on methods by G. Carbou and P. Fabrie for solutions of the Landau-Lifshitz equation.
Keywords
Cite
@article{arxiv.1608.02992,
title = {Existence of weak solutions to an evolutionary model for magnetoelasticity},
author = {Barbora Benešová and Johannes Forster and Chun Liu and Anja Schlömerkemper},
journal= {arXiv preprint arXiv:1608.02992},
year = {2016}
}