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| WEAK AND SMOOTH GLOBAL SOLUTION FOR LANDAU-LIFSHITZ-BLOCH-MAXWELL EQUATION |
| Boling Guo,Yongqian Han,Daiwen Huang,Fangfang Li |
| (Institute of Applied Physics and Computational Math., P.O. Box 8009, Beijing 100088, PR China;Institute of Applied Math., Academy of Math. and Systems Science, China Academy of Sciences, Beijing, 100190, PR China) |
| DOI： |
| Abstract: |
| This paper is devoted to investigate 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 $(H^{m+1},H^m,H^m)$ $(m\ge1)$, the existence and uniqueness of the global smooth solution are established. |
| Key words: Landau-Lifshitz-Bloch-Maxwell equation; global solution; para- magnetic-ferromagnetic transition; temperature-dependent magnetic theory; Landau-Lifshitz theory |