GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS

doi:10.1007/s10473-020-0511-0

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1335-1351.doi: 10.1007/s10473-020-0511-0

GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS

黄健骏¹, 姜正禄²

1. Department of Mathematics(Zhuhai), Sun Yat-Sen University, Zhuhai 519082, China;
2. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

收稿日期:2019-01-19 修回日期:2020-02-19 出版日期:2020-10-25 发布日期:2020-11-04
通讯作者: Zhenglu JIANG E-mail:mcsjzl@mail.sysu.edu.cn
作者简介:Jianjun HUANG,E-mail:mcshjj@hotmail.com
基金资助:
This work was supported by NSFC (11171356).

GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS

Jianjun HUANG¹, Zhenglu JIANG²

1. Department of Mathematics(Zhuhai), Sun Yat-Sen University, Zhuhai 519082, China;
2. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Received:2019-01-19 Revised:2020-02-19 Online:2020-10-25 Published:2020-11-04
Contact: Zhenglu JIANG E-mail:mcsjzl@mail.sysu.edu.cn
Supported by:
This work was supported by NSFC (11171356).

摘要/Abstract

摘要： This article extends the results of Arkeryd and Cercignani [6]. It is shown that the Cauchy problem for the relativistic Enskog equation in a periodic box has a global mild solution if the mass, energy and entropy of the initial data are finite. It is also found that the solutions of the relativistic Enskog equation weakly converge to the solutions of the relativistic Boltzmann equation in L¹ if the diameter of the relativistic particle tends to zero.

关键词: global existence, relativistic Enskog equation, relativistic Boltzmann equation

Abstract: This article extends the results of Arkeryd and Cercignani [6]. It is shown that the Cauchy problem for the relativistic Enskog equation in a periodic box has a global mild solution if the mass, energy and entropy of the initial data are finite. It is also found that the solutions of the relativistic Enskog equation weakly converge to the solutions of the relativistic Boltzmann equation in L¹ if the diameter of the relativistic particle tends to zero.

Key words: global existence, relativistic Enskog equation, relativistic Boltzmann equation

中图分类号:

76P05

黄健骏, 姜正禄. GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS[J]. 数学物理学报(英文版), 2020, 40(5): 1335-1351.

Jianjun HUANG, Zhenglu JIANG. GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1335-1351.

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GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS

GLOBAL EXISTENCE FOR THE RELATIVISTIC ENSKOG EQUATIONS

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