On the stability of the Ginzburg-Landau vortex - Archive ouverte HAL
Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2022

On the stability of the Ginzburg-Landau vortex

Résumé

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.

Dates et versions

hal-03263218 , version 1 (17-06-2021)

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Philippe Gravejat, Eliot Pacherie, Didier Smets. On the stability of the Ginzburg-Landau vortex. Proceedings of the London Mathematical Society, 2022, ⟨10.1112/plms.12475⟩. ⟨hal-03263218⟩
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