Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations |
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| Authors: | Jie Jiang Hao Wu BoLing Guo |
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| Institution: | 1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China
2. School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China
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| Abstract: | 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. |
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| Keywords: | time-dependent Ginzburg-Landau equations BCS-BEC crossover global attractor exponential attractor |
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