The critical velocity for vortex existence in a two-dimensional rotating Bose–Einstein condensate

We investigate a model corresponding to the experiments for a two-dimensional rotating Bose–Einstein condensate. It consists in minimizing a Gross–Pitaevskii functional defined in R2 under the unit mass constraint. We estimate the critical rotational speed Ω1 for vortex existence in the bulk of the condensate and we give some fundamental energy estimates for velocities close to Ω1.