Discrete time navier-stokes limit for the BGK Boltzmann equation

Consider the simplified Bathnagar Gross and Krook model of the Boltzmann equation [1]. The particular form of the entropy production allows to get sharp estimates for pertubations of global thermodynamical equilibrium. Then, following Bardos, Golse and Levermore [4], we can derive the discrete time Navier-Stokes equations, as soon as we have a bound from below for the macroscopic density. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.