The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary

I will talk about the inviscid limit for the Navier-Stokes equations in a half space (in both 2D and 3D case),  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.