一类耦合Ginzburg-Landau系统的局部极小解  

Locally Minimizing Solutions of a Two-component Ginzburg-Landau System

作　　者：熊晨 高琦 Xiong Chen;Gao Qi(Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院数学系,武汉430070

出　　处：《数学物理学报（A辑）》2023年第2期321-340,共20页Acta Mathematica Scientia

基　　金：国家自然科学基金(11931012,11871386);中央高校基本科研业务费专项基金(WUT:2020IB019)。

摘　　要：该文考虑耦合Ginzburg-Landau系统整体解中一类特殊的解—局部极小解的相关性质,证明了局部极小解的环绕度一定是n±∈{0,±1}.同时,该文还证明了局部极小解的两个分量中其中一个为零,而另一个不为零,即物理中的少核涡旋现象.In this paper,we consider a Ginzburg-Landau functional for a complex vector order parameterψ=[ψ+ψ_].In particular,we consider entire solutions in all R^(2),which are obtained by blowing up around vortices.Among the entire solutions we distinguish those which are locally minimizing solutions,and we show that locally minimizing solutions must have degrees n士G{0,±1}.By studying the local structure of these solutions,we also show that one component of the solution vanishes,but the other does not,which describes the coreless vortex phenomenon in physics.

关 键 词：椭圆方程组 局部极小解 变分法 

分 类 号：O175.2[理学—数学]