The paper is concerned with the analysis of an evolutionary model for magnetoviscoelastic materials in two dimensions. The model consists of a Navier-Stokes system featuring a dependence of the stress tensor on elastic and magnetic terms, a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the magnetization.First, we show that our model possesses global in time weak solutions, thus extending work by Benešová et al. 2018. Compared to that work, we include the stray field energy and relax the assumptions on the elastic energy density. Second, we prove the local-in-time existence of strong solutions. Both existence results are based on the Galerkin method. Finally, we show a weak-strong uniqueness property.

中文翻译：

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磁粘弹性演化模型的弱解和强解的数学分析

本文涉及二维磁粘弹性材料演化模型的分析。该模型包括一个Navier-Stokes系统（其特征在于应力张量与弹性和磁性项有关），一个用于形变梯度演化的正则化系统以及一个用于磁化动力学的Landau-Lifshitz-Gilbert系统。证明我们的模型拥有及时的全局弱解，从而扩展了Benešová等人的工作。2018年。与该工作相比，我们将杂散场能量包括在内，并放宽了对弹性能量密度的假设。其次，我们证明了强大的解决方案在本地存在。两种存在结果均基于Galerkin方法。最后，我们显示了弱强唯一性。