Averaging of 2D Navier–Stokes equations with singularly oscillating forces

Abstract

For ρ ∊ [0, 1) and ε > 0, the nonautonomous 2D Navier–Stokes equations with singularly oscillating external force are considered, together with the averaged equations formally corresponding to the limiting case ε = 0. Under suitable assumptions on the external force, the uniform boundedness of the related uniform global attractors is established, as well as the convergence of the attractors of the first system to the attractor of the second one as ε → 0+. When the Grashof number of the averaged equations is small, the convergence rate of to is controlled by Kε1−ρ.