# Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity

## TL;DR

This paper provides a comprehensive mathematical analysis of a two-dimensional evolutionary model for magnetoviscoelastic materials, establishing the existence of weak and strong solutions, and demonstrating weak-strong uniqueness.

## Contribution

It extends previous work by including stray field energy, relaxing elastic energy assumptions, and proving existence and uniqueness results for the model.

## Key findings

- Existence of global weak solutions including stray field energy.
- Local in time existence of strong solutions.
- Weak-strong uniqueness property established.

## Abstract

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 Bene\v{s}ov\'a 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.