Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier-Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T Caraballo et al., C. R. Acad. Sci. Paris, Set. I 342 (2006). (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.