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In this present paper, the existence of pullback attractors for the 2D Navier-Stokes equation with weak damping and continuous delay is considered; by virtue of the classical Galerkin method, we derive the existence and uniqueness of global weak and strong solutions. Using the Aubin-Lions lemma and some energy estimate in the Banach space with delay, we obtain the uniform bound and the existence of a uniform pullback absorbing ball for the solution’s semi-processes, and we conclude to the global attractors via verifying the pullback asymptotical compactness by the generalized Arzelà-Ascoli theorem.

Pullback attractors of 2D Navier-Stokes equations with weak damping and continuous delay