On the Convergence of the Uniform Attractor for the 2D Leray-α Model

Abstract

We consider a nonautonomous 2D Leray-$\alpha$ model of fluid turbulence. We prove the existence of the uniform attractor ${\mathcal{A}}^{\alpha }$. We also study the convergence of ${\mathcal{A}}^{\alpha }$ as $\alpha$ goes to zero. More precisely, we prove that the uniform attractor ${\mathcal{A}}^{\alpha }$ converges to the uniform attractor of the 2D Navier-Stokes system as $\alpha$ tends to zero.