  In this paper, we establish the short time inviscid limit of the
incompressible Navier-Stokes equations with critical Navier-slip boundary
conditions for analytic data on half-space, a boundary condition that is
physically derived from the hydrodynamic limit of the Boltzmann equations with
the Maxwell boundary conditions. The analysis is built upon the recent
framework developed by T. T. Nguyen and T. T. Nguyen (Arch. Ration. Mech.
Anal., 230(3):1103-1129, 2018.) in the case of the classical no-slip boundary
conditions. The novelty in this paper is to derive the precise pointwise bound
on the Green kernel for the Stokes problem with a nonlocal boundary condition
and to propagate the boundary layer behavior for vorticity.
