On the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half-plane

We consider the Navier-Stokes equations for viscous incompressible flows in the half-plane under the no-slip boundary condition. By using the vorticity formulation we prove the local-in-time convergence of the Navier-Stokes flows to the Euler flows outside a boundary layer and to the Prandtl flows in the boundary layer in the inviscid limit when the initial vorticity is located away from the boundary.