Weak and Smooth Global Solution for Landau-Lifshitz-Bloch-Maxwell Equation

Abstract

This paper is devoted to investigating the existence and uniqueness of the solution of Landau-Lifshitz-Bloch-Maxwell equation. The Landau-Lifshitz-Bloch-Maxwell equation, which fits well for a wide range of temperature, is used to study the dynamics of magnetization vector in a ferromagnetic body. If the initial data is in ($H$¹, $L$², $L$²), the existence of the global weak solution is established. If the initial data is in ($H$^$m$+1, $H$^$m$, $H$^$m$) ($m$ ≥ 1), the existence and uniqueness of the global smooth solution are established.