Existence and regularity of pullback attractors for a 3D non-autonomous Navier–Stokes–Voigt model with finite delay

Abstract

In this manuscript previous results [Nonlinearity 25(2012), 905–930] are extended to a non-autonomous 3D Navier–Stokes–Voigt model in which a forcing term contains memory effects. Under suitable assumptions on the function driving the delay time, the existence and uniqueness of weak solution are proved. Existence and relationships among pullback attractors in several phase-spaces are analyzed for two possible choices of the attracted universes, namely, the standard one of fixed bounded sets, and another one given by a tempered condition. Some regularity results for these attractors are also established. Compactness and attraction norms are strengthened. Since the model does not have a regularizing effect, obtaining asymptotic compactness for the associated process is a more involved task. Our proofs rely on a sharp use of the energy equality, an energy method, bootstrapping arguments and by using bi-space attractors results.