Weak and Smooth Global Solution for Landau-Lifshitz-Bloch-Maxwell Equation
Keywords:
Landau-Lifshitz-Bloch-Maxwell equation, global solution, paramagnetic-ferromagnetic transition, temperature-dependent magnetic theory, Landau-Lifshitz theory.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.