Local minimality of -valued and -valued Ginzburg–Landau vortex solutions in the unit ball

  • Radu Ignat

    Université de Toulouse, CNRS, UPS IMT, Toulouse, France
  • Luc Nguyen

    University of Oxford, UK
Local minimality of $\mathbb{R}^N$-valued and $\mathbb{S}^N$-valued Ginzburg–Landau vortex solutions in the unit ball $B^N$ cover
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Abstract

We study the existence, uniqueness and minimality of critical points of the form of the functional for with on . We establish a necessary and sufficient condition on the dimension and the parameters and for the existence of an escaping vortex solution with . We also establish its uniqueness and local minimality. In particular, when , we prove the local minimality of the degree-one vortex solution for the Ginzburg–Landau (GL) energy for every and . Similarly, when , we prove the local minimality of the degree-one escaping vortex solution to an -valued GL model in micromagnetics for all and .

Cite this article

Radu Ignat, Luc Nguyen, Local minimality of -valued and -valued Ginzburg–Landau vortex solutions in the unit ball . Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 3, pp. 663–724

DOI 10.4171/AIHPC/84