Finite dimensional global and exponential attractors for a coupled time-dependent Ginzburg-Landau equations for atomic Fermi gases near the BCS-BEC crossover

Details Finite dimensional global and exponential attractors for a coupled time-dependent Ginzburg-Landau equations for atomic Fermi gases near the BCS-BEC crossover Finite dimensional global and exponential attractors for a coupled time-dependent Ginzburg-Landau equations for atomic Fermi gases near the BCS-BEC crossover

2010-11-03

arxiv.org/abs/1011.0793v1

Sci. China Math., 55(1) (2012), 141-157

Mathematics

Analysis of PDEs

Scientific paper

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover. First, we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses the 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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