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Séminaire de EDP - Physique Mathématique

Minimality of the vortex solution for Ginzburg-Landau systems

Radu Ignat

( Institut de Mathématiques de Toulouse )

Toulouse et via zoom

le 07 mai 2024 à 11:00

We consider the standard Ginzburg-Landau system for N-dimensional maps defined in the unit ball for some parameter eps>0. For a boundary data corresponding to a vortex of topological degree one, the aim is to prove the (radial) symmetry of the ground state of the system. We show this conjecture in any dimension N≥7 and for every eps>0, and then, we also prove it in dimension N=4,5,6 provided that the admissible maps are curl-free. This is part of joint works with L. Nguyen, M. Rus, V. Slastikov and A. Zarnescu.

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