PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

doi:10.1016/S0252-9602(11)60272-5

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 727-748.doi: 10.1016/S0252-9602(11)60272-5

• 论文 • 上一篇

PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

寇艳蕾|丁时进

Department of Mathematics, South China Normal University, Guangzhou |510631, China

收稿日期:2010-02-01 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
The second author is partially supported by the National Natural Science Foundation of China (10471050), Guangdong Provincial
Natural Science Foundation (031495), and National 973 Project (2006CB805902)

PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

KOU Yan-Lei, DING Shi-Jin

Department of Mathematics, South China Normal University, Guangzhou |510631, China

Received:2010-02-01 Online:2011-03-20 Published:2011-03-20
Supported by:
The second author is partially supported by the National Natural Science Foundation of China (10471050), Guangdong Provincial
Natural Science Foundation (031495), and National 973 Project (2006CB805902)

摘要/Abstract

摘要：

We study the partial regularity of weak solutions to the 2-dimensional Landau-Lifshitz equations coupled with time dependent
Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic
Hausdorff measure, we prove the uniform local C^∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points.

关键词: Landau-Lifshitz-Maxwell equations, ginzburg-landau approximations, Hausdorff measure, partial regularity

Abstract:

We study the partial regularity of weak solutions to the 2-dimensional Landau-Lifshitz equations coupled with time dependent Maxwell equations by Ginzburg-Landau type approximation. Outside an energy concentration set of locally finite 2-dimensional parabolic Hausdorff measure, we prove the uniform local C^∞ bounds for the approaching solutions and then extract a subsequence converging to a global weak solution of the Landau-Lifshitz-Maxwell equations which are smooth away from finitely many points.

Key words: Landau-Lifshitz-Maxwell equations, ginzburg-landau approximations, Hausdorff measure, partial regularity

中图分类号:

35J55

寇艳蕾, 丁时进. PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION[J]. 数学物理学报(英文版), 2011, 31(2): 727-748.

KOU Yan-Lei, DING Shi-Jin. PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION[J]. Acta mathematica scientia,Series B, 2011, 31(2): 727-748.

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PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

PARTIAL COMPACTNESS FOR LANDAU-LIFSHITZ MAXWELL EQUATION IN TWO-DIMENSION

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