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For a Bose-Einstein condensate placed in a rotating trap and confined in thez axis, we set a framework of study for the Gross-Pitaevskii energy in theThomas Fermi regime. We investigate an asymptotic development of the energy,the critical velocities of nucleation of vortices with respect to a smallparameter $\ep$ and the location of vortices. The limit $\ep$ going to zerocorresponds to the Thomas Fermi regime. The non-dimensionalized energy issimilar to the Ginzburg-Landau energy for superconductors in the high-kappahigh-field limit and our estimates rely on techniques developed for this latterproblem. We also take the advantage of this similarity to develop a numericalalgorithm for computing the Bose-Einstein vortices. Numerical results andenergy diagrams are presented.Comment: 10pages 9 figure

Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime