Slow Motion Collisions and Phase Vortex Interaction in the Two-Dimensional Parabolic Ginzburg-Landau Dynamics

Thursday, October 28, 2004 - 2:40pm - 3:30pm
EE/CS 3-180
Fabrice Bethuel (Université de Paris VI (Pierre et Marie Curie))
The talk is based on a joint work with D.Smets and G. Orlandi, in which we describe a natural framework for the vortex dynamics the parabolic complexGinzburg-landau equation on the plane. This general setting does not rely on any assumption of well-preparedness and has the advantage to be valid even after possible collision times. We analyze carefully collisions leading to annihilation, and identify a new phenomenon, the phase-vortex interaction, related to persistency of low frequency oscillations, and leading to an unexpected drift in the motion of vortices.

I will also discuss open issues, as the splitting of multiple degree vortices,, collisions without annihilation, ...