  We establish the validity of the Euler$+$Prandtl approximation for solutions
of the Navier-Stokes equations in the half plane with 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 $L^{1}$-type norm for the vorticity of the error term in the
expansion Navier-Stokes$-($Euler$+$Prandtl$)$. An important ingredient in the
proof is the propagation of local analyticity for the Euler equation, a result
of independent interest.
