On the homogenization principle in a time-periodic problem for the Navier–Stokes equations with rapidly oscillating mass force

Abstract

We study the behavior of the set of time-periodic solutions of the three-dimensional system of Navier–Stokes equations in a bounded domain as the frequency of the oscillations of the right-hand side tends to infinity. It is established that the set of periodic solutions tends to the solution set of the homogenized stationary equation.