Large time behavior for the fractional Ginzburg-Landau equations near the BCS-BEC crossover regime of Fermi gases
In this paper, we consider the fractional Ginzburg-Landau equations near the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensate (BCS-BEC) crossover of atomic Fermi gases. This fractional Ginzburg-Landau equations can be viewed as a generalization of the integral differential equations proposed by Machida and Koyama (Phys.
Rev. A 74:033603,
By using the Galerkin method and a priori estimates, together with the properties of Sobolev spaces, we first establish the existence and uniqueness of weak solutions to these equations and then we prove the existence of global attractors.