Entropy production for ellipsoidal BGK model of the Boltzmann equation

Seok-Bae  Yun

doi:10.3934/krm.2016009

Article Contents

2016, Volume 9, Issue 3: 605-619. Doi: 10.3934/krm.2016009

This issue Previous Article Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma Next Article

Entropy production for ellipsoidal BGK model of the Boltzmann equation

Seok-Bae Yun^1,

1.
Department of mathematics, Sungkyunkwan University, Suwon 440-746

Received: September 30, 2015

Revised: December 31, 2015

Published: August 2016

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Abstract

The ellipsoidal BGK model (ES-BGK) is a generalized version of the original BGK model, designed to yield the correct Prandtl number in the Navier-Stokes limit. In this paper, we make two observations on the entropy production functional of the ES-BGK model. First, we show that the Cercignani type estimate holds for the ES-BGK model in the whole range of relaxation parameter $-1/2<\nu<1$. Secondly, we observe that the ellipsoidal relaxation operator satisfies an unexpected sign-definite property. Some implications of these observations are also discussed.

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Mathematics Subject Classification: Primary: 35Q20, 82C40; Secondary: 35B45.

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