ASYMPTOTIC ANALYSIS OF OSEEN TYPE EQUATIONS IN A CHANNEL AT SMALL VISCOSITY

Our object in this article is to study the boundary layer appearing at large Reynolds number (small viscosity epsilon) in Oseen type equatio ns in space dimension two in a channel. These are Navier-Stokes equati ons linearized around a fixed velocity flow: we study the convergence as epsilon --> 0 to the inviscid type equations, we define the correct ors needed to resolve the boundary layer and obtain convergence result s valid up to the boundary; we study also the behavior of the boundary layer when simultaneously time and the Reynolds number tend to infini ty in which case the boundary layer tends to pervade the whole domain. To avoid the difficulties related to complicated geometries we restri ct-ourselves to the flow in a channel. This article extends previous r esults [22] concerning the Stokes equations, i.e. the Navier-Stokes eq uations linearized around rest. An important fact which appears here a nd which did not appear in [22], is the mixing of the layers in the ta ngential direction which is due to the transport term.