Average Process of Fractional Navier–Stokes Equations with Singularly Oscillating Force

Abstract

The averaging process between two-dimensional fractional Navier–Stokes equations driven by a singularly oscillating external force and the averaged equations corresponding to the limiting case are investigated. The uniform boundedness of the global attractors for a fractional Navier–Stokes equation with a singularly external force is established. Furthermore, these global attractors converge uniformly to the attractor of the averaged equations under suitable assumptions on the singularly external force, and the explicit convergence rate of the global attractors is guaranteed.