H2H2-boundedness of the pullback attractors for non-autonomous 2D Navier–Stokes equations in bounded domains

We prove some regularity results for the pullback attractors of a non-autonomous 2D Navier–Stokes model in a bounded domain ΩΩ of R2R2. We establish a general result about (H2(Ω))2∩V(H2(Ω))2∩V-boundedness of invariant sets for the associate evolution process. Then, as a consequence, we deduce that, under adequate assumptions, the pullback attractors of the non-autonomous 2D Navier–Stokes equations are bounded not only in VV but also in (H2(Ω))2(H2(Ω))2.