Duke Mathematical Journal

Limiting vorticities for the Ginzburg-Landau equations

Etienne Sandier and Sylvia Serfaty

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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.

Article information

Duke Math. J., Volume 117, Number 3 (2003), 403-446.

First available in Project Euclid: 26 May 2004

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Zentralblatt MATH identifier

Primary: 82D55: Superconductors
Secondary: 35B25: Singular perturbations 35J20: Variational methods for second-order elliptic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 58E50: Applications


Sandier, Etienne; Serfaty, Sylvia. Limiting vorticities for the Ginzburg-Landau equations. Duke Math. J. 117 (2003), no. 3, 403--446. doi:10.1215/S0012-7094-03-11732-9. https://projecteuclid.org/euclid.dmj/1085598401

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