Boundary Layer for a Non-Newtonian Flow Over a Rough Surface

We analyse how small irregularities of the solid surface effects the steady flow of a general viscous fluid at larger scales. In particular we consider generalised Stokes system for incompressible non-Newtonian fluids of power-law type with zero Dirichlet boundary conditions when the surface of boundary is rough. Namely, it contains microscopic surface irregularities and an amplitude, and a wavelength of oscillations is described by a small parameter which converges to zero. Our aim is to derive effective boundary conditions a wall law on a smoothed boundary which gives a small approximation error. To this end we study corresponding boundary layer problem. This is a result of a joint research with David Gérad-Varet.