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

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  • 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.
    Mathematics Subject Classification: Primary: 35R10, 35B40, 47H20, 58F39, 73K70.

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