Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping.

Abstract

In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier Stokes equations with damping. We consider two cases, depending on the values of the parameter β controlling the damping term. First, we prove that for β ≥ 4 weak solutions are unique and establish the existence of the global attractor for the corresponding semigroup. Second, for 3 ≤ β < 4 we define a multivalued dynamical systems and prove the existence of the global attractor as well. Finally, some numerical simulations are performed.