Stable configurations in superconductivity: Uniqueness, multiplicity, and vortex-nucleation
type: Item
instance of: scholarly article
title: Stable configurations in superconductivity: Uniqueness, multiplicity, and vortex-nucleation
zbMATH Open document ID: 0959.35154
author: S. Serfaty
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-04-26T00:00:00Z
review text: Essential improvements of previous results by the same author [Commun. Contemp. Math. 1, 213-254 (1999; Zbl 0944.49007)] concerning the solutions of the two-dimensional Ginzburg-Landau equation \[ -\nabla^2_A u=\kappa^2u(1-|u|^2),\quad -*dh=(iu,d_Au) \] which describes the energy of a superconductor, put in a uniform magnetic field \(h_{\text{ex}}\), are presented. The most important problem is the appearance of zeros of \(u\) (the vortex structure) which depends on the level of the parameter \(h_{\text{ex}}\) (a function of \(\kappa\)). The article involves many subtle results: the existence and uniqueness of Messner-type (i.e., stable and vortexless) solutions, the existence of solutions with \(n\) vortices of degree one for higher values of \(h_{\text{ex}}\), and the estimates of the energy of the vortex-nucleation (the energy barrier of the Messner solution).
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 82D55
zbMATH DE Number: 1419583
zbMATH Keywords: vortices
zbMATH Keywords: Meissner solution
zbMATH Keywords: nucleation
zbMATH Keywords: energy level
reviewed by: Jan Chrastina
MaRDI profile type: Publication
full work available at URL: s002050050177
OpenAlex ID: W1991496322
DOI: 10.1007/S002050050177
description: scientific article; zbMATH DE number 1419583