15 April 2003 Limiting vorticities for the Ginzburg-Landau equations
Etienne Sandier, Sylvia Serfaty
Duke Math. J. 117(3): 403-446 (15 April 2003). DOI: 10.1215/S0012-7094-03-11732-9


We study the asymptotic limit of solutions of the Ginzburg-Landau equations in two dimensions with or without magnetic field. We first study the Ginzburg-Landau system with magnetic field describing a superconductor in an applied magnetic field, in the "London limit" of a Ginzburg-Landau parameter $\kappa$ tending to $\infty$. We examine the asymptotic behavior of the "vorticity measures" associated to the vortices of the solution, and we prove that passing to the limit in the equations (via the "stress-energy tensor") yields a criticality condition on the limiting measures. This condition allows us to describe the possible locations and densities of the vortices. We establish analogous results for the Ginzburg-Landau equation without magnetic field.


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Etienne Sandier. Sylvia Serfaty. "Limiting vorticities for the Ginzburg-Landau equations." Duke Math. J. 117 (3) 403 - 446, 15 April 2003. https://doi.org/10.1215/S0012-7094-03-11732-9


Published: 15 April 2003
First available in Project Euclid: 26 May 2004

zbMATH: 1035.82045
MathSciNet: MR1979050
Digital Object Identifier: 10.1215/S0012-7094-03-11732-9

Primary: 82D55
Secondary: 35B25 , 35J20 , 35Q55 , 58E50

Rights: Copyright © 2003 Duke University Press

Vol.117 • No. 3 • 15 April 2003
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