Abstract: The object of this article is to study the boundary layer appearing at large Reynolds number (small viscosity ε) incompressible Navier-Stokes Equation in a cylinder in space dimension three. These are Navier-Stokes
equations linearized around a fixed velocity flow: the authors study the
convergence as ε→ 0 to the inviscid type equations, the authors define the correctors needed to resolve the boundary layer and obtain convergence results valid up to the boundary and the authors also study the behavior of the boundary layer when, simultaneously, time and the Reynolds number tend to infinity, in which case the boundary layer tends to pervade the whole domain.

Key words: Boundary layer, incompressible Navier-Stokes equation, small viscosity