PARTIAL REGULARITY FOR THE 2-DIMENSIONAL WEIGHTED LANDAU-LIFSHITZ FLOW  

作　　者：Ye Yunhua Ding Shijin 

机构地区：[1]Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631, China

出　　处：《Journal of Partial Differential Equations》2007年第1期11-29,共19页偏微分方程（英文版）

基　　金：The second author is partially supported by the National Natural Science Foundation of China （Grant No.10471050）, the National 973 project （Grant No. 2006CB805902） and by Guangdong Provincial Natural Science Foundation （Grant No.031495）.

摘　　要：We consider the partial regularity of weak solutions to the weighted Landau-Lifshitz flow on a 2-dimensional bounded smooth domain by Ginzburg-Landau type approximation. Under the energy smallness condition, we prove the uniform local C^∞ bounds for the approaching solutions. This shows that the approximating solutions are locally uniformly bounded in C^∞（Reg（{uε}）∩（Ω^-×R^＋）） which guarantee the smooth convergence in these points. Energy estimates for the approximating equations are used to prove that the singularity set has locally finite two-dimensional parabolic Hausdorff measure and has at most finite points at each fixed time. From the uniform boundedness of approximating solutions in C^∞（Reg（{uε}）∩（Ω^-×R^＋））, we then extract a subsequence converging to a global weak solution to the weighted Landau-Lifshitz flow which is in fact regular away from finitely many points.

关 键 词：Landau-Lifshitz equations Ginzburg-Landau approximations Hausdorff measure partial regularity. 

分 类 号：O175.29[理学—数学]