Ginzburg-Landau方程极小能量解存在性的新证明

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 299-306.

Ginzburg-Landau方程极小能量解存在性的新证明

黄德成¹, 陈守信²

1 信阳职业技术学院数学与计算机学院河南信阳 464000;
2 河南大学数学与统计学院, 现代数学研究所河南开封 475004

收稿日期:2016-06-13 修回日期:2016-10-22 出版日期:2017-04-26 发布日期:2017-04-26
通讯作者: 陈守信 E-mail:chensx@henu.edu.cn
作者简介:黄德成,huangdecheng123@126.com
基金资助:
国家自然科学基金（11471100，11471099）和河南省科技厅基础与前沿项目基金（142300410110）

New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations

Huang Decheng¹, Chen Shouxin²

1 School of Mathematics and Computers, Xinyang Vocational and Technical College, Henan Xinyang 464000;
2 Institute of Contemporary Mathmatics, School of Mathematics and Statistics, Henan University, Henan Kaifeng 475004

Received:2016-06-13 Revised:2016-10-22 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (11471100, 11471099) and the Foundation and Frontier Project of Department of Science and Technology of Henan Province (142300410110)

摘要/Abstract

摘要： 对R²上带有外磁场或一般流源场的Ginzburg-Landau方程组，借助于Hardy型不等式，利用直接变分的方法重新证明了其极小能量解的存在性，且该解满足Coulomb规范.

关键词: Ginzburg-Landau方程, 变分法, Hardy型不等式, 解的存在性

Abstract: In this paper we use a direct variational method, with the help of Hardy type inequality, to give a new proof for the existence of minimizing energy solutions for the Ginzburg-Landau equations in R² coupled with an external magnetic field or a source current. Moreover, the solution satisfies the Coulomb gauge.

Key words: Ginzburg-Landau equations, Variational method, Hardy type inequality, Existence of solutions

中图分类号:

O175.25

黄德成, 陈守信. Ginzburg-Landau方程极小能量解存在性的新证明[J]. 数学物理学报, 2017, 37(2): 299-306.

Huang Decheng, Chen Shouxin. New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations[J]. Acta mathematica scientia,Series A, 2017, 37(2): 299-306.

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