We study the minimizers of a magnetic two-dimensional nonlinear Schrödinger
energy functional in a quadratic trapping potential, describing a rotating
Bose–Einstein condensate. We derive an effective Thomas–Fermi-like model in the
rapidly rotating limit where the centrifugal force compensates the confinement and
available states are restricted to the lowest Landau level. The coupling constant of
the effective Thomas–Fermi functional is linked to the emergence of vortex
lattices (the Abrikosov problem). We define it via a low-density expansion of
the energy of the corresponding homogeneous gas in the thermodynamic
limit.
