Communications in Mathematical Sciences

Volume 17 (2019)

Number 4

About viscous approximations of the bitemperature Euler system

Pages: 1135 – 1147



Denise Aregba-Driollet (Institut de Mathématiques de Bordeaux, Talence, France)

Stéphane Brull (Institut de Mathématiques de Bordeaux, Talence, France)


This paper is devoted to the study of the construction of a viscous approximation of the nonconservative bitemperature Euler system. Starting from a BGK model coupled with Ampère and Poisson equations proposed in [D.Aregba, J. Breil, S. Brull, B. Dubroca, and E. Estibals, Math. Models Numer. Anal., 52(4):1353–1383, 2018], we perform a Chapman–Enskog expansion up to order $1$ leading to a Navier-Stokes system. Next, we prove that this system is compatible with the entropy of the bitemperature Euler system.


Chapman–Enskog expansion, viscous system, nonconservative system

2010 Mathematics Subject Classification

35Q35, 35Q83, 82D10

Received 29 November 2018

Accepted 28 May 2019

Published 25 October 2019