2021/06/04 by Philippe Gravejat, Gravejat, Philippe, Eliot Pacherie +3 · 1 citation
Computer Science · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation
paper · doi:10.48550/arxiv.2106.02511
openalex publication_date 2021/06/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.