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In this paper we obtain some results on the existence of solution, and of pullback attractors, for a 2D Navier-Stokes model with finite delay studied in [4] and [6]. Actually, we prove a result of existence and uniqueness of solution under less restrictive assumptions than in [4]. More precisely, we remove a condition on square integrable control of the memory terms, which allows us to consider a bigger class of delay terms (for instance, just under a measurability condition on the delay function leading the delayed time). After that, we deal with dynamical systems in suitable phase spaces within two metrics, the L 2 norm and the H 1 norm. Moreover, we prove that under these assumptions, pullback attractors not only of fixed bounded sets but also of a set of tempered universes do exist. Finally, from comparison results of attractors we establish relations among them, and under suitable additional assumptions we conclude that these families of attractors are in fact the same object.

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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 C([−h, 0]; V ). 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.

In this paper we consider a non-autonomous Navier-Stokes-Voigt model, to which a continuous process can be associated. We study the existence and relationship between minimal pullback attractors for this process in two different frameworks, namely, for the universe of fixed bounded sets, and also for another universe given by a tempered condition.Since the model does not have a regularizing effect, to obtaining asymptotic compactness for the process is a more involved task. We prove this in a relatively simple way just by using an energy method. Our results simplify -and in some aspects generalize-some of those obtained previously for the autonomous and non-autonomous cases, since for example in Section 4, regularity is not required for the boundary of the domain and the force may take values in V . Under additional suitable assumptions, regularity results for these families of attractors are also obtained, via bootstrapping arguments. Finally, we also conclude some results concerning the attraction in the D(A) norm.