# Limiting vorticities for the Ginzburg-Landau equations

Etienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticle

### 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 language English (US) 403-446 44 Duke Mathematical Journal 117 3 https://doi.org/10.1215/S0012-7094-03-11732-9 Published - Apr 15 2003

### Fingerprint

Ginzburg-Landau Equation
Vorticity
Limiting
Magnetic Field
Ginzburg-Landau
Vortex
Asymptotic Limit
Superconductor
Criticality
Two Dimensions
Tensor
Asymptotic Behavior
Energy

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Limiting vorticities for the Ginzburg-Landau equations. / Sandier, Etienne; Serfaty, Sylvia.

In: Duke Mathematical Journal, Vol. 117, No. 3, 15.04.2003, p. 403-446.

Research output: Contribution to journalArticle

Sandier, Etienne ; Serfaty, Sylvia. / Limiting vorticities for the Ginzburg-Landau equations. In: Duke Mathematical Journal. 2003 ; Vol. 117, No. 3. pp. 403-446.
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