The Uniform Attractors for the Nonhomogeneous 2D Navier-Stokes Equations in Some Unbounded Domain. (3rd February 2008) - Wu, Delin
Abstract : We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domainΩ with nonhomogeneous boundary conditions. We apply the so-called uniformlyω -limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assumingf ∈ L loc 2 ( ( 0, T ) ; L 2 ( Ω ) ), which is translation compact andφ ∈ C b 1 ( ℝ + ; H 2 ( ℝ 1 × { ± L } ) ) asymptotically almost periodic, we establish the existence of the uniform attractor inH 1 (Ω ).