Dissipative solutions to a system for the flow of magnetoviscoelastic materials

TL;DR

This paper proves the global existence of dissipative solutions for a magnetoviscoelastic system in two and three dimensions, extending previous results to include magnetization dynamics governed by the Landau-Lifshitz-Gilbert equation.

Contribution

It introduces the concept of dissipative solutions to establish global existence for a complex coupled magnetoviscoelastic system, including magnetization evolution.

Findings

Global existence of solutions in 2D and 3D

Extension of previous viscoelastic results to magnetization systems

Use of dissipative solutions framework

Abstract

We address the question of global in time existence of solutions to a magnetoviscoelastic system with general initial data. We show that the notion of dissipative solutions allows to prove such an existence in two and three dimensions. This extends an earlier result for the viscoelastic subsystem to the setting which includes the magnetization vector and its evolution in terms of a Landau-Lifshitz-Gilbert equation.