Dynamics Of A 3D Navier-Stokes Equations With Damping

In this paper, we investigate the dynamics of the following three dimensional Navier-Stokes equations with damping α|u|β-1u(α> 0,β> 3),We first prove the existence of pullback attractors in H and V, then we show that the usual (H, H) Dλ-pullback attractor indeed can pullback attract the Dλ class in L2+δ-norm for any δ ∈ [0,+∞).