Entropy production estimate for the ES-BGK model with the correct Prandtl number

Abstract

In this paper, we establish the entropy-entropy production estimate for the ES-BGK model, a generalized version of the BGK model of the Boltzmann equation introduced for better approximation in the Navier-Stokes limit. Our result improves the previous entropy production estimate [39] in that (1) the full range of Prandtl parameters $-1/2\le \nu <1$ including the critical case $\nu =-1/2$ is covered, and (2) a sharper entropy production bound is obtained. An explicit characterization of the coefficient of the entropy-entropy production estimate is also presented.

13 pages