Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2024

Stability of the vortex in micromagnetics and related models

Résumé

We consider line-energy models of Ginzburg-Landau type in a two-dimensional simplyconnected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the configuration a vortex. We prove a quantitative version of this statement in the class of C 1,1 domains, improving on previous results by Lorent. In particular, the deviation of the domain from a disk is controlled by a power of the energy, and that power is optimal. The main tool is a Lagrangian representation introduced by the second author, which allows to decompose the energy along characteristic curves.

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hal-04128800 , version 1 (14-06-2023)

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Xavier Lamy, Elio Marconi. Stability of the vortex in micromagnetics and related models. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2024, 25 (4), pp. 2051-2100. ⟨10.2422/2036-2145.202209_012⟩. ⟨hal-04128800⟩
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