Existence of weak solutions to an evolutionary model for magnetoelasticity

Barbora Benešová, Johannes Forster, Chun Liu, Anja Schlömerkemper

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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, 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 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.

Original languageEnglish (US)
Pages (from-to)1200-1236
Number of pages37
JournalSIAM Journal on Mathematical Analysis
Volume50
Issue number1
DOIs
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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