Higher Order Approximations to the Navier–Stokes Flow in a Rough Boundary Domain

Abstract

We consider an incompressible flow governed by the nonlinear Navier–Stokes equations with periodic boundary conditions in a domain with periodic roughness. Approximations to the flow up to the second order are deduced starting from a modification of the analogous flow in a simpler truncated domain, i.e. its extension to a series with respect to the amplitude of the rough part of the flow domain. The rigorous estimates for the approximations are given.