  We study the long time behavior of solutions to a nonlinear partial
differential equation arising in the description of trapped rotating
Bose-Einstein condensates. The equation can be seen as a hybrid between the
well-known nonlinear Schr\"odinger/Gross-Pitaevskii equation and the
Ginzburg-Landau equation. We prove existence and uniqueness of global in-time
solutions in the physical energy space and establish the existence of a global
attractor within the associated dynamics. We also obtain basic structural
properties of the attractor and an estimate on its Hausdorff and fractal
dimensions.
