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.