Homogenization of stratified dilatant fluid

In this paper we study the behavior of the stationary magnetic hydrodynamical boundary layer of a dilatant fluid flowing through a porous obstacle. We consider a family of boundary value problems with a small parameter where micro-inhomogeneities are concentrated on the boundary of the domain (the original velocity profile depends on a small parameter). We construct an averaged problem and prove convergence of the solution of the original problem to that of the averaged one. Thus we describe the effective behavior of the micro-inhomogeneous fluid.