  We consider the zero viscosity limit of the incompressible Navier-Stokes
equations with non-slip boundary condition in the half-space for the initial
vorticity located away from the boundary. By using the vorticity formulation
and Cauchy-Kowaleskaya theorem, Maekawa proved the local in time convergence of
the Navier-Stokes equations in the half- plane to the Euler equations outside a
boundary layer and to the Prandtl equations in the boundary layer. In this
paper, we develop the direct energy method to generalize Maekawa's result to
the half-space.

Analysis of PDEs