Global solutions of the Landau--Lifshitz--Baryakhtar equation

TL;DR

This paper proves the existence and uniqueness of global solutions to the Landau--Lifshitz--Baryakhtar equation, a model in magnetism accounting for nonlocal damping and finite temperature effects.

Contribution

It establishes the mathematical well-posedness of the LLBar equation, including weak, strong, and regular solutions, and discusses their continuity properties.

Findings

Proved existence of global weak solutions.

Established uniqueness of solutions.

Analyzed H"older continuity of solutions.

Abstract

The Landau--Lifshitz--Baryakhtar (LLBar) equation is a generalisation of the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch equations which takes into account contributions from nonlocal damping and is valid at moderate temperature below the Curie temperature. Therefore, it is used to explain some discrepancies between the experimental observations and the known theories in various problems on magnonics and magnetic domain-wall dynamics. In this paper, the existence and uniqueness of global weak, strong, and regular solutions to LLBar equation are proven. H\"older continuity of the solution is also discussed.