Calculus of Variations and Geometric Measure Theory
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F. Bethuel - G. Orlandi - D. Smets

Dynamics of multiple-degree Ginzburg-Landau vortices

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


Published Paper

Inserted: 17 mar 2007
Last Updated: 24 dec 2009

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


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.

Keywords: Ginzburg-Landau, vortex dynamics, Kirchoff-Onsager


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