Sur la concentration de masse d'un condensat de Bose-Einstein.

Abstract

We consider two-dimensional Bose–Einstein condensates with attractive interac- tion, described by the Gross–Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies a < a∗ = ||Q||2, where Q is the unique pos- itive radial solution of −∆u−u + u3 = 0 in R2. We present a detailed analysis of the behavior of minimizers as a approaches a∗, where all the mass concentrates at a global minimum of the trapping potential. Mathematics Subject Classification (2010). 35Q40, 46N50, 82D50.