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arXiv · 1608.02992

Existence of weak solutions to an evolutionary model for magnetoelasticity

Barbora Benešová·Johannes Forster·Chun Liu·Anja Schlömerkemper
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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.

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Barbora Benešová, Johannes Forster, Chun Liu, Anja Schlömerkemper. 2016-08-09. Existence of weak solutions to an evolutionary model for magnetoelasticity. https://arxiv.org/abs/1608.02992

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