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We study the long time behavior of solutions to a nonlinear partial differential equation arising in the mean-field description of trapped rotating Bose-Einstein condensates. The equation can be seen as a hybrid between the well-known nonlinear Schrödinger/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 alsodoi:10.4310/dpde.2017.v14.n1.a2 fatcat:ecgvktw33nhclorfjfu7e5dwqi