# Dynamics of multiple-degree Ginzburg-Landau vortices

created by orlandi on 17 Mar 2007
modified on 24 Dec 2009

[BibTeX]

Published Paper

Inserted: 17 mar 2007
Last Updated: 24 dec 2009

Journal: Comm. Math. Phys.
Volume: 272
Number: 1
Pages: 229-261
Year: 2007

Abstract:

For the two dimensional complex parabolic Ginzburg-Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff-Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data.