Existence of Weak Solutions to an Evolutionary Model for Magnetoelasticity
Existence of Weak Solutions to an Evolutionary Model for Magnetoelasticity
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DOI：
10.1137/17m1111486
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
B. Benesová;Johannes Forster;Chun Liu;A. Schlömerkemper
中科院分区：
文献类型：
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作者：
B. Benesová;Johannes Forster;Chun Liu;A. Schlömerkemper
证明了磁弹性材料演化模型弱解的存在性。该模型是措辞在欧拉坐标系中，并特别包括（i）一个Navier-Stokes方程，其中包括磁和弹性项的应力张量通过变分方法获得，（ii）一个正则化的传输方程的变形梯度和（iii）的Landau-Lifshitz-吉尔伯特方程的磁化的动力学。证明是建立在一个Galerkin方法和一个固定点的论点。它是基于F的想法。H.林和第三作者的液晶流动的系统建模方法以及G。Carbou和P. Fabrie求解Landau-Lifshitz方程。
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.