The Navier–Stokes limit for the Boltzmann equation

Abstract

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