Global attractors for non-Newtonian equations on BCS-BEC crossover

This paper considers the global attractor problem for the non-Newtonian equations on BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.These non-Newtonian equations can be translated into the time-dependent Ginzburg-Landau equations.In order to establish the attractors, we first prove the existence and uniqueness theorem of weak solutions by the standard Faedo-Galerkin approximation method.Then, we establish some suitable prior estimates of the weak solutions by combining Gagliardo-Nirenberg inequality, Agmon's inequality and Gronwall inequality, etc.Finally, using the existence theorem of the global attractor, we prove that there exists a compact global attractor for the time dependent Ginzburg-Landau equations of BCS-BEC crossover on atomic fermi gases near the Feshbach resonance.