Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics

Abstract

In this article, we describe a natural framework for the vortex dynamics in the complex-valued parabolic Ginzburg-Landau equation in ${\displaystyle {\mathbb{R}}^2}$. This general setting does not rely on any assumption of well-preparedness and has the advantage of being valid even after collision times. We carefully analyze collisions leading to annihilation. A new phenomenon is identified, the phase-vortex interaction, which is related to the persistence of low-frequency oscillations and leads to an unexpected drift in the motion of vortices