  We address the inviscid limit for the Navier-Stokes equations in a half
space, with initial datum that is analytic only close to the boundary of the
domain, and has finite Sobolev regularity in the complement. We prove that for
such data the solution of the Navier-Stokes equations converges in the
vanishing viscosity limit to the solution of the Euler equation, on a constant
time interval.
