Uniform attractors for three-dimensional Navier-Stokes equations with nonlinear damping

摘要

This paper is concerned with the three-dimensional non-autonomous Navier-Stokes equation with nonlinear damping in 3D bounded domains. When the external force f(0)(x, t) is translation compact in L-loc(2)(R; H), alpha > 0, 7/2 <= beta <= 5 and initial data u(tau) is an element of V, we give a series of uniform estimates on the solutions. Based on these estimates, we prove the family of processes {U-f(t, tau)}, f is an element of H(f(0)), is (V x H(f(0)), V)-continuous. At the same time, by making use of Ascoli-Arzela theorem, we find {U-f(t,tau)}, f is an element of H(f(0)), is (V, H-2(Omega))-uniformly compact. So, using semiprocess theory, we obtain the existence of (V, V)-uniform attractor and (V, H-2(Omega))-uniform attractor. And we prove the (V, V)-uniform attractor is actually the (V, H-2(Omega))-uniform attractor. (C) 2014 Elsevier Inc. All rights reserved.