# Uniqueness of solutions for a mathematical model for magneto-viscoelastic flows

## TL;DR

This paper proves the conditions under which weak solutions to a magneto-viscoelastic flow model are unique, extending known Navier-Stokes results to coupled systems involving deformation and magnetization.

## Contribution

It establishes weak-strong uniqueness for a coupled PDE system modeling magnetoelastic materials, linking conditions to classical Navier-Stokes criteria.

## Key findings

- Weak solutions are unique in two dimensions.
- Weak solutions satisfying Prodi-Serrin conditions are unique in three dimensions.
- The results extend Navier-Stokes uniqueness criteria to magneto-viscoelastic flows.

## Abstract

We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation gradient and for the magnetization obtained from a special case of the micromagnetic energy. It turns out that the conditions on uniqueness coincide with those for the well-known Navier-Stokes equations in bounded domains: weak solutions are unique in two spatial dimensions, and weak solutions satisfying the Prodi-Serrin conditions are unique among all weak solutions in three dimensions. That is, we obtain the so-called weak-strong uniqueness result in three spatial dimensions.