Some stationary weak solutions to inhomogeneous Landau-Lifshitz equations in three dimensions  

作　　者：FANG Dao-yuan LI Tai-long XUE Ru-ying 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2007年第6期949-956,共8页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10571158);the Natural Science Foundation of Zheji-ang Province, China (No. Y605076)

摘　　要：In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.

关 键 词：Landau-Lifshitz equation Stationary condition Hausdorff measure 

分 类 号：O175[理学—数学] O48[理学—基础数学]