On the stability of the Ginzburg-Landau vortex
Analysis of PDEs
2021-06-07 v1
Abstract
We introduce a functional framework taylored to investigate the minimality and stability properties of the Ginzburg-Landau vortex of degree one on the whole plane. We prove that a renormalized Ginzburg-Landau energy is well-defined in that framework and that the vortex is its unique global minimizer up to the invariances by translation and phase shift. Our main result is a nonlinear coercivity estimate for the renormalized energy around the vortex, from which we can deduce its orbital stability as a solution to the Gross-Pitaevskii equation, the natural Hamiltonian evolution equation associated to the Ginzburg-Landau energy.
Keywords
Cite
@article{arxiv.2106.02511,
title = {On the stability of the Ginzburg-Landau vortex},
author = {Philippe Gravejat and Eliot Pacherie and Didier Smets},
journal= {arXiv preprint arXiv:2106.02511},
year = {2021}
}