Pull-back attractors for three-dimensional Navier—Stokes—Voigt equations in some unbounded domains

Abstract

We study the first initial–boundary-value problem for the three-dimensional non-autonomous Navier–Stokes–Voigt equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Faedo–Galerkin method. We then show the existence of a unique minimal finite-dimensional pull-back $\smash{\mathcal D_\sigma}$-attractor for the process associated with the problem, with respect to a large class of non-autonomous forcing terms. We also discuss relationships between the pull-back attractor, the uniform attractor and the global attractor.