Dynamical behaviour of non-autonomous 2D Navier–Stokes equations with singularly oscillating external force

Abstract

The purpose of this article is to analyse the dynamical behaviour of solutions of the non-autonomous 2D Navier–Stokes equations with singularly oscillating external force of the form: . First, we prove the existence of uniform attractor in for equations with external force non-translation compact. Then we prove that if the function g 1(z, t) satisfies the Divergence condition (Definition 3.1), then the uniform attractor is convergent to uniform attractor of the averaged equations in the sense of Hausdorff distance in L 2(Ω).