caa a22 4500 467891354 CHVBK 20180406152750.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10955-005-8087-6 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8087-6 Bobylev A. Department of Mathematics, Karlstad University, 651 88, Karlstad, Sweden aut Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations [Elektronische Daten] [A. Bobylev] It is well-known that the classical Chapman-Enskog procedure does not work at the level of Burnett equations (the next step after the Navier-Stokes equations). Roughly speaking, the reason is that the solutions of higher equations of hydrodynamics (Burnett's, etc.) become unstable with respect to short-wave perturbations. This problem was recently attacked by several authors who proposed different ways to deal with it. We present in this paper one of possible alternatives. First we deduce a criterion for hyperbolicity of Burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases. Then we discuss in more detail the problem of truncation of the Chapman-Enskog expansion and show that the way of truncation is not unique. The general idea of changes of coordinates (based on analogy with the theory of dynamical systems) leads finally to nonlinear Hyperbolic Burnett Equations (HBEs) without using any information beyond the classical Burnett equations. It is proved that HBEs satisfy the linearized H-theorem. The linear version of the problem is studied in more detail, the complete Chapman-Enskog expansion is given for the linear case. A simplified proof of the Slemrod identity for Burnett coefficients is also given. Springer Science + Business Media, Inc., 2005 Boltzmann equation nationallicence Chapman-Enskog method nationallicence Burnett equations nationallicence hyperbolicity nationallicence Perturbation theory nationallicence Hydrodynamics nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 371-399 0022-4715 124:2-4<371 2006 124 10955 https://doi.org/10.1007/s10955-005-8087-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8087-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bobylev A. Department of Mathematics, Karlstad University, 651 88, Karlstad, Sweden aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/2-4(2006-08-01), 371-399 0022-4715 124:2-4<371 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer