The attractors for the nonhomogeneous nonautonomous Navier–Stokes equations

In this paper, we consider the attractors for the two-dimensional nonautonomous Navier–Stokes equations in nonsmooth bounded domain Ω with nonhomogeneous boundary condition u = ϕ on ∂Ω. Assuming f = f (x, t) ∈ L2 loc((0,T );D(Aα/4)), which is translation compact and ϕ ∈ L∞(∂Ω), we establish the existence of the uniform attractor in L2(Ω) and D(A1/4). © 2005 Elsevier Inc. All rights reserved.