In this lecture we will study the behavior for small viscosity of the Navier-Stokes equations in a channel, when the wall are permeable (non characteristic case). Convergence is proved to the Euler equations for the linearized and the nonlinear case, for dimension two and three (for a limited time in the nonlinear case); and the appropriate correctors describing the boundary layers are constructed. The methodology is also reminescent of the multideck boundary layer theory by Stewartson and others.