Inserted: 17 mar 2007
Last Updated: 24 dec 2009
Journal: Comm. Math. Phys.
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