Stability of the vortex in micromagnetics and related models

2022/09/16 by Xavier Lamy, Lamy, Xavier, Elio Marconi +1
Computer Science · Mathematics · Physics and Astronomy · #35F21 #49J45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Magnetic properties of thin films #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2209.09662

openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected 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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