Homogenization of boundary layer of pseudo-plastic fluid in the presence of rapidly oscillating external forces

In this paper, we study the homogenization problem for equations of magnetohydrodynamic boundary layer of pseudo-plastic fluid. It is assumed that the external flow velocity and the external magnetic field are described by oscillating functions and the frequency depends on a small parameter. In von Mises variables and in Cartesian variables, we construct the homogenized problem, establish strong convergence of solutions in a special norm, and estimate the rate of this convergence. We show that in von Mises variables the convergence rates in different norms are of different orders of smallness.