Dynamics of a globally modified Navier–Stokes model with double delay

Abstract

This paper investigates the dynamics of a class of three-dimensional globally modified Navier-Stokes equations with double delay in the forcing and convective terms. We first prove the well-posedness of solutions of such system, which enables us to establish suitable non-autonomous dynamical systems. We then show the existence and uniqueness of pullback attractors for the associated dynamical systems. Finally, by using the generalized Banach limit, we construct a family of invariant Borel probability measures, which are supported on the pullback attractors.