  The existence and uniqueness of the analytic solutions to the nonlinear
Prandtl equations with Robin boundary condition on a half space are proved,
based on an application of abstract Cauchy-Kowalewski theorem. These equations
arise in the inviscid limit of incompressible Navier-Stokes equations with
Navier-slip boundary condition in which the slip length is square root of
viscosity, as formally derived in [26].
