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

We analyze the effect of a rough surface on shear thinning and shear thickening fluids, modeled by power law stress tensors. The roughness is modeled by a small wavelength and small amplitude oscillation, parametrized by eps. We study the boundary layer corrector near the rough surface, and provide error estimates in terms of eps for the associated wall laws. With regards to previous studies, Mathematical difficulties arise from the nonlinearity of the corrector equations.