Boundary Value Problems
Volume 2008 (2008), Article ID 831746, 12 pages
doi:10.1155/2008/831746

The uniform attractors for the nonhomogeneous 2D Navier-Stokes equations in some unbounded domain

Abstract

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f∈Lloc2((0,T);L2(Ω)), which is translation compact and φ∈Cb1(ℝ+;H2(ℝ1×{±L})) asymptotically almost periodic, we establish the existence of the uniform attractor in H1(Ω).