The Navier-Stokes Limit of the Boltzmann equation for bounded collision kernels

The present work establishes a Navier-Stokes limit for the Boltzmann equation considered over the infinite spatial domain R³. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations whose limit points (in the w-L¹ topology) are governed by Leray solutions of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. Pure Appl. Math. 46(5), 667-753 (1993)] for the steady case, and in Lions-Masmoudi [Arch. Ration. Mech. Anal. 158(3), 173-193 (2001)] for the time-dependent case.