Boundary layers associated with the incompressible Navier-Stokes equations:The non characteristic case

In this lecture, we will study the behavior for small viscosity of the Navier-Stokes equations in a channel when the walls are permeable (noncharacteristic 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 reminiscent of the multideck boundary layer theory by Stewartson and others.