On the Euler + Prandtl Expansion for the Navier-Stokes Equations

We establish the validity of the Euler+ Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with the Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an L¹-type norm for the vorticity of the error term in the expansion Navier-Stokes- (Euler+ Prandtl).