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Linear Stability of Hyperbolic Moment Models for Boltzmann Equation

Part of:Partial differential equationsPartial differential equations on manifolds; differential operatorsTime-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  09 May 2017

Yana Di,
Yuwei Fan,
Ruo Li and
Lingchao Zheng
Yana Di*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, NCMIS, AMSS, Chinese Academy of Sciences, Beijing 100190, China
Yuwei Fan*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
Ruo Li*
Affiliation:
HEDPS & CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, China
Lingchao Zheng*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
*
*Corresponding author. Email addresses:yndi@lsec.cc.ac.cn (Y. Di), ywfan@pku.edu.cn (Y. Fan), rli@math.pku.edu.cn (R. Li), lczheng@pku.edu.cn (L. Zheng)
*Corresponding author. Email addresses:yndi@lsec.cc.ac.cn (Y. Di), ywfan@pku.edu.cn (Y. Fan), rli@math.pku.edu.cn (R. Li), lczheng@pku.edu.cn (L. Zheng)
*Corresponding author. Email addresses:yndi@lsec.cc.ac.cn (Y. Di), ywfan@pku.edu.cn (Y. Fan), rli@math.pku.edu.cn (R. Li), lczheng@pku.edu.cn (L. Zheng)
*Corresponding author. Email addresses:yndi@lsec.cc.ac.cn (Y. Di), ywfan@pku.edu.cn (Y. Fan), rli@math.pku.edu.cn (R. Li), lczheng@pku.edu.cn (L. Zheng)

Abstract

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Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the convection term in Boltzmann equation. We in this paper studied the regularized models with the presentation of collision terms. It is proved that the regularized models are linearly stable at the local equilibrium and satisfy Yong's first stability condition with commonly used approximate collision terms, and particularly with Boltzmann's binary collision model.

Keywords

Boltzmann equationGrad's moment methodhyperbolic moment equationlinear stability

MSC classification

Secondary:82C40: Kinetic theory of gases58J45: Hyperbolic equations35B35: Stability

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 2 , May 2017, pp. 255 - 277
Copyright
Copyright © Global-Science Press 2017 

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