Estimates for the asymptotic expansion of a viscous fluid satisfying Navier's law on a rugous boundary

In a previous paper, we have studied the asymptotic behavior of a viscous fluid satisfying Navier's law on a periodic rugous boundary of period ε and amplitude δ _ε , with δ _ε / ε tending to zero. In the critical size, δ _ε ～ ε ^3/2, in order to obtain a strong approximation of the velocity and the pressure it is necessary to consider a boundary layer term in the corresponding ansatz. The purpose of this paper is to estimate the approximation given by this ansatz. Copyright © 2011 John Wiley & Sons, Ltd.