Motion of the Ginzburg-Landau vortices for the mixed flow with convective forcing

TL;DR

This paper analyzes the vortex motion in a mixed Ginzburg-Landau flow with convective forcing, deriving a new law that incorporates nonlinear forcing terms influenced by initial conditions.

Contribution

It introduces a novel vortex motion law for the mixed Ginzburg-Landau flow with convective derivatives, accounting for additional nonlinear forcing terms.

Findings

Derived the vortex motion law with nonlinear forcing terms.

Showed the law is uniquely determined by initial PDE terms.

Proved results under initial data close to optimal.

Abstract

We consider the mixed Ginzburg-Landau flow that is supplemented with convective derivatives of the unknown function. We show that the associated vortex motion law is the mixed flow of the renormalized energy with new nonlinear forcing terms. These terms are uniquely determined by the extra terms in the initial PDE. Our proof relies on the assumption that the initial data are close to optimal.