复值 Ginzburg-Landau 方程组的无粘性极限

数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 347-358.

复值 Ginzburg-Landau 方程组的无粘性极限

邹冉(),廖梦兰^*()

河海大学数学学院南京 210098

收稿日期:2024-05-07 修回日期:2024-09-09 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 廖梦兰 E-mail:231362010028@hhu.edu.cn;liaoml@hhu.edu.cn
作者简介:邹冉，E-mail:231362010028@hhu.edu.cn
基金资助:
国家自然科学基金(U2340221);国家自然科学基金(12401290);江苏省自然科学基金(BK20230036);江苏省自然科学基金(BK20221497);江苏省自然科学基金(BK20230946)

The Inviscid Limit of the Ginzburg-Landau System

Ran Zou(),Menglan Liao^*()

School of Mathematics, Hohai University, Nanjing 210098

Received:2024-05-07 Revised:2024-09-09 Online:2025-04-26 Published:2025-04-09
Contact: Menglan Liao E-mail:231362010028@hhu.edu.cn;liaoml@hhu.edu.cn
Supported by:
NSFC(U2340221);NSFC(12401290);NSFC of Jiangsu Province(BK20230036);NSFC of Jiangsu Province(BK20221497);NSFC of Jiangsu Province(BK20230946)

摘要/Abstract

摘要：

该文主要研究 Ginzburg-Landau 方程组的整体无粘性极限, 其中初值属于 $L^2(\mathbb{R}^n)\times L^2(\mathbb{R}^n)$ 或 $H^1(\mathbb{R}^n)\times H^1(\mathbb{R}^n)$ . 具体来说, 研究 Ginzburg-Landau 方程组与非线性薛定谔方程组解的差值, 利用能量估计对差值进行处理, 从而得到 Ginzburg-Landau 方程组的无粘性极限是非线性薛定谔方程组的解.

关键词: Ginzburg-Landau 方程组, 无粘性极限, 能量估计, 薛定谔方程组

Abstract:

This paper mainly studies the global inviscid limit of the Ginzburg-Landau system while the initial data is taken in $L^2(\mathbb{R}^n){\times}L^2(\mathbb{R}^n)\operatorname{or}H^1(\mathbb{R}^n){\times}H^1(\mathbb{R}^n).$ Specifically, we investigate the difference between the solution of the Ginzburg-Landau system and the nonlinear Schrödinger system, and use energy estimate to deal with the difference．It is obtained that the inviscid limit of the solution of the Ginzburg-Landau system is the solution of the nonlinear Schrödinger system．

Key words: Ginzburg-Landau system, inviscid limit, energy estimate, Schr?dinger system

中图分类号:

O175.24

邹冉,廖梦兰. 复值 Ginzburg-Landau 方程组的无粘性极限[J]. 数学物理学报, 2025, 45(2): 347-358.

Ran Zou,Menglan Liao. The Inviscid Limit of the Ginzburg-Landau System[J]. Acta mathematica scientia,Series A, 2025, 45(2): 347-358.

参考文献 8

[1]	Guo B, Jiang M, Li Y. Ginzburg-Landau Equations. Beijing: Science Press, 2020
[2]	Li Y S, Guo B L. Global existence of solutions to the derivative 2D Ginzburg-Landau equation. J Math Anal Appl, 2000, 249: 412-432
[3]	Wu J. The inviscid limit of the complex Ginzburg-Landau equation. J Differential Equations, 1998, 142(2): 413-433
[4]	Bechouche P, Jungel A. Inviscid limits of the complex Ginzburg-Landau equation. Comm Math Phys, 2000, 214(1): 201-226
[5]	Wang B. The limit behavior of solutions for the Cauchy problem of the complex Ginzburg-Landau equation. Comm Pure Appl Math, 2002, 55(4): 481-508
[6]	Huang C, Wang B. Inviscid limit for the energy-critical complex Ginzburg-Landau equation. J Funct Anal, 2008, 255(3): 681-725
[7]	Nouaili N, Zaag H. Construction of a blow-up solution for the complex Ginzburg-Landau equation in a critical case. Arch Ration Mech Anal, 2018, 228(3): 995-1058
[8]	Porretta A. A note on the Sobolev and Gagliardo-Nirenberg inequality when $p>N$ . Adv Nonlinear Stud, 2020, 20(2): 361-371 doi: 10.1515/ans-2020-2086

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