Fluid-dynamic limit for the Ruijgrok–Wu model of the Boltzmann equation

In this paper we consider the fluid-dynamic limit for the Ruijgrok–Wu model derived from the Boltzmann equation. We use new technique developed in [S. Hwang, A.E. Tzavaras, Kinetic decomposition of approximate solutions to conservation laws: Applications to relaxation and diffusiondispersion approximations, Comm. Partial Differential Equations 27 (2002) 1229–1254] in order to get the convergence. First, we obtain the approximate transport equation for the given kinetic model. Then using the averaging lemma, we obtain the convergence. This paper shows how to relate the given kinetic model with the averaging lemma to get the convergence.  2005 Elsevier Inc. All rights reserved.