  In this paper we shall consider the Navier-Stokes equations in the half plane
with Euler-type initial conditions, i.e. initial conditions which have a
non-zero tangential component at the boundary. Under analyticity assumptions
for the data, we shall prove that the solution exists for a small time
independent of the viscosity. The solution is constructed through a composite
asymptotic expansion involving the solutions of the Euler and Prandtl
equations, plus an error term. The norm of the error goes to zero with the
square root of the viscosity. The Prandtl solution contains a singular term,
which influences the regularity of the error. The error term is written as the
sum of a first order Euler correction, a first order Prandtl correction, and a
further error term. The use of an analytic setting is mainly due to the Prandtl
equation.
