Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays

In this paper we strengthen some results on the existence and properties of pullback attractors for a 2D Navier-Stokes model with finite delay formulated in [Caraballo and Real, J. Differential Equations 205 (2004), 271--297]. Actually, we prove that under suitable assumptions, pullback attractors not only of fixed bounded sets but also of a set of tempered universes do exist. Moreover, thanks to regularity results, the attraction from different phase spaces also happens in . Finally, from comparison results of attractors, and under an additional hypothesis, we establish that all these families of attractors are in fact the same object.