H 2 -boundedness of the pullback attractors for non-autonomous 2D-Navier-Stokes equations in bounded domains Julia Garc´ ıa-Luengo, Pedro Mar´ ın-Rubio, Jos´ e Real Dpto. de Ecuaciones Diferenciales y An´alisis Num´ erico, Universidad de Sevilla, Apdo. de Correos 1160, 41080 Sevilla, Spain Abstract We prove some regularity results for the pullback attractors of a non-autonomous 2D-Navier-Stokes model in a bounded domain Ω of R 2 . We establish a general result about (H 2 (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 V but also in (H 2 (Ω)) 2 . Key words: 2D-Navier-Stokes equations, pullback attractors, invariant sets, H 2 -regularity. Mathematics Subject Classifications (2010): 35B41, 35B65, 35Q30 ⋆ Corresponding author: Jos´ e Real This work has been partially supported by Ministerio de Ciencia e Innovaci´on (Spain) under project MTM2008-00088, and Junta de Andaluc´ ıa grant P07-FQM- 02468. J.G.-L. is a fellow of Programa de FPU del Ministerio de Educaci´on. Email addresses: luengo@us.es (Julia Garc´ ıa-Luengo), pmr@us.es (Pedro Mar´ ın-Rubio), jreal@us.es (Jos´ e Real). Preprint submitted to Nonlinear Analysis 4 March 2011