Boundary layer for a non-Newtonian flow over a rough surface (Q2821654)

This paper deals with the effect of rough walls on a non-Newtonian fluid flow. The governing system of equations is made complete by a standard no-slip condition at the top and bottom boundary of the channel; the goal is to study the asymptotic behavior of the Navier-Stokes solution as \(\varepsilon\to 0\), where \(\varepsilon\) is a small parameter parametrizing the bottom surface. The discussion then focuses on to the derivation of equations satisfied by the leading term in the asymptotic expansion, to their solution, to show convergence of the boundary layer term to a constant field away from the boundary, to obtain error estimates, and to derive from there appropriate wall laws.