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We consider the 3D Navier-Stokes equations in the upper half space $\mathbbH^3_+$ with periodic boundary conditions in the horizontal directions. We provethe inviscid limit holds in the topology $L^\infty([0, T]; L^2(\mathbb H^3_+))$assuming the initial datum is analytic in the region $\{(x, y, z)\in\mathbbH^3_+: 0\le z\le 1+\mu_0\}$ for some positive $\mu_0$ and has Sobolevregularity in the complement.

The 3D inviscid limit problem with data analytic near the boundary