Ginzburg-Landau Vortex and Mean Curvature Flow with External Force Field

作     者：Huai Yu JIAN Yan Nan LIU 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing 100084 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2006年第22卷第6期

页      面：1831-1842页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National 973-Project and Basic Research Grant of Tsinghua University 

主　　题：system of parabolic equations Ginzburg-Landau vortex mean curvature flow 

摘      要：This paper is devoted to the study of the vortex dynamics of the Cauchy problem for a parabolic Ginzburg Landau system which simulates inhomogeneous type II superconducting materials and three-dimensional superconducting thin films having variable thickness. We will prove that the vortex of the problem is moved by a codimension k mean curvature flow with external force field. Besides, we will show that the mean curvature flow depends strongly on the external force, having completely different phenomena from the usual mean curvature flow.