Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations  

作　　者：JIANG Jie WU Hao GUO BoLing 

机构地区：[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

出　　处：《Science China Mathematics》2012年第1期141-157,共17页中国科学：数学（英文版）

基　　金：partially supported by National Natural Science Foundation of China (Grant No.11001058);Specialized Research Fund for the Doctoral Program of Higher Education;the Fundamental Research Funds for the Central Universities

摘　　要：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 phase-space 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.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.

关 键 词：time-dependent Ginzburg-Landau equations BCS-BEC crossover global attractor exponentialattractor 

分 类 号：O175.29[理学—数学] O511[理学—基础数学]