EXISTENCE OF WEAK SOLUTIONS TO AN EVOLUTIONARY MODEL FOR MAGNETOELASTICITY

被引：31

作者：

Benesova, Barbora ^{[1
]}

Forster, Johannes ^{[1
]}

Liu, Chun ^{[2
]}

Schloemerkemper, Anja ^{[1
]}

机构：

[1] Univ Wurzburg, Inst Math, D-97074 Wurzburg, Germany

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 01期

关键词：

magnetoelasticity; Eulerian coordinates; existence of weak solutions; Landau Lifshitz-Gilbert equation; EQUATIONS; MAGNETOSTRICTION; MICROMAGNETICS; INSULATORS; SENSORS; SYSTEMS; STRESS; FLUIDS; FLOWS;

D O I：

10.1137/17M1111486

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, 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 fixedpoint argument. It is based on ideas from Lin and the third author for systems modeling the flow of liquid crystals as well as on methods by Carbou and Fabrie for solutions of the Landau Lifshitz equation.

引用

页码：1200 / 1236

页数：37

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