Limiting vorticities for the Ginzburg-Landau equations

Etienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticlepeer-review

Abstract

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 κ tending to ∞. 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.

Original languageEnglish (US)
Pages (from-to)403-446
Number of pages44
JournalDuke Mathematical Journal
Volume117
Issue number3
DOIs
StatePublished - Apr 15 2003

ASJC Scopus subject areas

  • Mathematics(all)

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