Mardi 23 avril 2013
Batiment Fermat, amphi I, à 9h30
Oranisateurs : Amandine Aftalion, Luc Robbiano
- Christos Sourdis (University of Crete) : The ground state of a Gross-Pitaevskii energy in the Thomas-Fermi limit
|We study the ground state which minimizes a Gross-Pitaevskii energy with general non-radial trapping potential, in the Thomas-Fermi limit where a small parameter tends to zero. This ground state plays an important role in the mathematical treatment of recent experiments on the phenomenon of Bose-Einstein condensation, and in the study of various types of solutions to nonhomogeneous defocusing nonlinear Schrodinger equations. Many of these applications require delicate estimates for the behavior of the ground state near the boundary of the condensate, in the vicinity of which the ground state develops irregular behavior in the form of a steep corner layer.
We utilize a perturbation argument to go beyond the classical Thomas-Fermi approximation and accurately approximate the layer by the Hastings-McLeod solution of the Painleve-II equation.
This is a joint work with G. Karali.
Journée Equations aux dérivées partielles et controle – avril 2013