The Global Attractor for the 2d Navier-stokes Flow on Some Unbounded Domains

We extend previous results on the existence of the global attractor for the 2D Navier-Stokes equations on some unbounded domains in the sense that the forcing term need not lie in any weighted space nor is the boundary of the domain required to be smooth. The existence of the global attractor is obtained on arbitrary open sets such that the Poincaré inequality holds and for forces in the natural dual space V ′. The proof is based on the energy equation and the concept of asymptotic compactness. An estimate of the Hausdorff and fractal dimensions of the attractor is also given.