THE THREE-DIMENSIONAL INVISCID LIMIT PROBLEM WITH DATA ANALYTIC NEAR THE BOUNDARY

We consider the three-dimensional Navier-Stokes equations in the upper half space H-+(3) with periodic boundary conditions in the horizontal directions. We prove the inviscid limit holds in the topology L-infinity ([0, T]; L-2 (H-+(3)) assuming the initial datum is analytic in the region {(x,y,z) is an element of H-3+ 0 <= z <= 1 + mu(0)} for some positive mu(0) and has Sobolev regularity in the complement.