Entropy production estimates for the polyatomic ellipsoidal BGK model

TL;DR

This paper investigates entropy production estimates in the polyatomic ellipsoidal BGK model, revealing different behaviors depending on a parameter, and identifies the equilibrium states toward which the system converges.

Contribution

It provides new entropy production estimates for the polyatomic ellipsoidal BGK model, highlighting the dependence on the parameter  and the resulting bifurcation of equilibrium states.

Findings

Distinct entropy production estimates for different  ranges

Identification of bifurcating equilibrium states

Analysis of asymptotic behavior of the distribution function

Abstract

We study the entropy production estimate for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the time evolution of polyatomic particle systems. An interesting dichotomy is observed between $0<\theta\leq 1$ and $\theta=0$: In each case, a distinct target Maxwellians should be chosen to estimate the entropy production functional from below by the relative entropy. The time asymptotic equilibrium state toward which the distribution function stabilizes bifurcates accordingly.