# American Institute of Mathematical Sciences

May  2006, 15(2): 559-578. doi: 10.3934/dcds.2006.15.559

## Pullback and forward attractors for a 3D LANS$-\alpha$ model with delay

 1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain 2 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain

Received  February 2005 Revised  September 2005 Published  March 2006

We analyze the asymptotic behaviour of a 3D Lagrangian averaged Navier-Stokes $\alpha$-model (3D LANS$-\alpha$) with delays. In fact, we apply the theory of pullback attractors to ensure the existence of a pullback attractor, and at the same time, we also prove the existence of a uniform (forward) attractor in the sense of Chepyzhov and Vishik. Instead of working directly with the 3D LANS$-\alpha$ model, we establish a general theory for an abstract delay model and then we apply the general results to our particular situation.
Citation: Tomás Caraballo, Antonio M. Márquez-Durán, José Real. Pullback and forward attractors for a 3D LANS$-\alpha$ model with delay. Discrete & Continuous Dynamical Systems, 2006, 15 (2) : 559-578. doi: 10.3934/dcds.2006.15.559
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