Pullback attractors for a two-dimensional Navier–Stokes model in an infinite delay case

We prove the existence of solutions for a Navier–Stokes model in two dimensions with an external force containing infinite delay effects in the weighted space Cγ(H)Cγ(H). Then, under additional suitable assumptions, we prove the existence and uniqueness of a stationary solution and the exponential decay of the solutions of the evolutionary problem to this stationary solution. Finally, we study the existence of pullback attractors for the dynamical system associated to the problem under more general assumptions.