A non-autonomous 3D Lagrangian averaged Navier-Stokes-$\alpha$ model with oscillating external force and its global attractor

Abstract

In this article, we consider a non-autonomous three-dimensional Lagrangian averaged Navier-Stokes-$\alpha$ model with a singulary oscillating external force depending on a small parameter $ \epsilon$. We prove the existence of the uniform global attractor $A^\epsilon$. Furthermore, using the method of [15] in the case of the two-dimensional Navier-Stokes systems, we study the convergence of $A^\epsilon $ as $\epsilon$ goes to zero.