Uniqueness of solutions for the Ginzburg-Landau model of superconductivity in three spatial dimensions
type: Item
instance of: scholarly article
title: Uniqueness of solutions for the Ginzburg-Landau model of superconductivity in three spatial dimensions
zbMATH Open document ID: 1043.35049
author: Bixiang Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-04T00:00:00Z
review text: This paper is devoted to study the uniqueness of weak solutions to the time-dependent Ginzburg-Landau (TDGL for short) model of superconductivity in three spatial dimensions. Here the author first establishes the \(L^p\) regularity of solutions and then, based on the regularity, shows the uniqueness of weak solutions for the periodic TDGL equations with any \(L^p\) \((p\geq 4)\) initial data. Existence for various \(L^p\) initial data was proved by \textit{S. Wang} and \textit{M.-Q. Zhan} [Nonlinear Anal., Theory Methods Appl. 36 B, No. 6, 661--677 (1999; Zbl 0919.35128)] and the author and \textit{N. Su} [Proc. R. Soc. Edinb., Sect. A, Math. 129, 627--639 (1999; Zbl 0940.35045)].
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 82D55
zbMATH DE Number: 1763692
zbMATH Keywords: \(L^p\) regularity
zbMATH Keywords: uniqueness of weak solutions
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7183
OpenAlex ID: W2049947495
cites work: On a non‐stationary Ginzburg–Landau superconductivity model
cites work: Global existence and uniqueness of solutions of the time-dependent ginzburg-landau model for superconductivity
cites work: On an evolutionary system of ginzburg-landau equations with fixed total magnetic flux
cites work: Asymptotic behaviour of the solutions of an evolutionary Ginzburg-Landau superconductivity model
cites work: Ginzburg-Landau dynamics with a time-dependent magnetic field
cites work: Dynamics of the Ginzburg-Landau equations of superconductivity
cites work: Macroscopic Models for Superconductivity
cites work: Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity
cites work: Determining nodes for the Ginzburg-Landau equations of superconductivity
cites work: Gevrey class regularity for the solutions of the Ginzburg-Landau equations of superconductivity
cites work: Time dependent Ginzburg-Landau equations of superconductivity
cites work: Lp solutions to the time-dependent Ginzburg–Landau equations of superconductivity
cites work: Existence of the solutions for the Ginzburg–Landau equations of superconductivity in three spatial dimensions
cites work: Equivalent Norms for Sobolev Spaces
DOI: 10.1006/JMAA.2000.7183
description: scientific article; zbMATH DE number 1763692