Regularity of pullback attractors and attraction in H1 in arbitrarily large finite intervals for 2D Navier-Stokes equations with infinite delay

In this paper we strengthen some results on the existence and properties of pullback attractors for a non-autonomous 2D Navier-Stokes model with infinite delay. Actually we prove that under suitable assumptions, and thanks to regularity results, the attraction also happens in the H1 norm for arbitrarily large finite intervals of time. Indeed, from comparison results of attractors we establish that all these families of attractors are in fact the same object. The tempered character of these families in H1 is also analyzed