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

The Uniform Attractors for the Nonhomogeneous 2D Navier-Stokes Equations in Some Unbounded Domain

Delin Wu

 College of Science, China Jiliang University, Hangzhou 310018, China
Received 14 November 2006; Revised 10 May 2007; Accepted 10 January 2008

Recommended by Roger Temam

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).