VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION  

作　　者：温焕尧 丁时进 

机构地区：[1]School of Mathematical Sciences, South China Normal University

出　　处：《Acta Mathematica Scientia》2010年第3期949-962,共14页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(10471050);the National 973 Project of China (2006CB805902);University Special Research Fund for Ph.DProgram (20060574002);Guangdong Provincial Natural Science Foundation (7005795, 031495)

摘　　要：In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Cinzburg-Landau equation in a smooth bounded domain Ω （R^2,that is ,Эtuε=j,k=1∑2（ajkЭxkuε）xj＋ε^2^-b（x）（1-｜uε｜^2）uε,x∈Ω,and conclude that each vortex,bj（t）（j=1,2,…,N）satisfies dt^-dbj（t）=-（a（bj（t））^-a1k（bj（t））Эxka（bj（t））,a（aj（t））^-a2k（bj（t））Эxka（bj（t）））,where a（x）=√a11a22-a12^2. We prove that all the vortices are pinned together to the critical points of a（x）. Furthermore, we prove that these critical points can not be the maximum points.In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Cinzburg-Landau equation in a smooth bounded domain Ω （R^2,that is ,Эtuε=j,k=1∑2（ajkЭxkuε）xj＋ε^2^-b（x）（1-｜uε｜^2）uε,x∈Ω,and conclude that each vortex,bj（t）（j=1,2,…,N）satisfies dt^-dbj（t）=-（a（bj（t））^-a1k（bj（t））Эxka（bj（t））,a（aj（t））^-a2k（bj（t））Эxka（bj（t）））,where a（x）=√a11a22-a12^2. We prove that all the vortices are pinned together to the critical points of a（x）. Furthermore, we prove that these critical points can not be the maximum points.

关 键 词：Anisotropic Ginzburg-Landau equation Gronwall inequality vortex dynamics 

分 类 号：O175[理学—数学]