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 , which is translation compact and φ∈L∞(∂Ω), we establish the existence of the uniform attractor in L2(Ω) and .