On boundary layer of Newtonian fluid, flowing on a rough surface and percolating through a perforated obstacle

In the paper we consider the behavior of electroconductive fluid percolating through a perforated obstacle and flowing over a rough surface. We consider a family of boundary value problems with a small parameter, in which the micro inhomogeneity concentrates on the boundary (the initial velocity profile depends on the small parameter and the surface along which the boundary layer is considered, is rapidly oscillating). The homogenized problem is obtained and the convergence of a solution of the initial problem to the solution of the homogenized problem is proved. Thus, the effective behavior of this microinhomogeneous fluid is described.