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arXiv · 2106.02511

On the stability of the Ginzburg-Landau vortex

Philippe Gravejat·Eliot Pacherie·Didier Smets
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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.

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Philippe Gravejat, Eliot Pacherie, Didier Smets. 2021-06-04. On the stability of the Ginzburg-Landau vortex. https://arxiv.org/abs/2106.02511

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