On the convergence of the uniform attractor of 2D NS- model to the uniform attractor of 2D NS system

First, the existence of uniform attractors for nonautonomous 2D NS- α model with normal force term on the T 2 torus in L l o c 2 ( R ; V ′ ) is proved. Then we study the relations between the uniform attractor of 2D NS- α model and 2D NS system. We prove that the uniform attractor of the 2D NS- α model converges to the 2D NS system as α tends to zero.