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

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. Hölder continuity of the solution is also discussed.