Séminaire MAC
# Minimality of the vortex solution for Ginzburg-Landau systems

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Amphi Schwartz (IMT)
### Amphi Schwartz

#### IMT

https://cnrs.zoom.us/j/91463344125?pwd=WVBtNjUzSnBqWXI3SDlYZTN5akc2dz09

Description

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.

Organized by

Romain Duboscq, David Lafontaine