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Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations. (English) Zbl 1239.35026
Summary: We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover. First, we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phasespace which possesses a global attractor. Then we establish the existence of an exponential attractor. As a consequence, we show that the global attractor is of finite fractal dimension.

35B41 Attractors
37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents
81V45 Atomic physics
35Q56 Ginzburg-Landau equations
Full Text: DOI arXiv
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