EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM

doi:10.1007/s10473-022-0108-x

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 155-171.doi: 10.1007/s10473-022-0108-x

EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM

吴菲^1,2, 王泽军^1,2

1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China;
2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China

收稿日期:2020-08-06 修回日期:2021-05-18 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Fei WU,E-mail:wufei003@nuaa.edu.cn E-mail:wufei003@nuaa.edu.cn
作者简介:Zejun WANG,E-mail:wangzejun@gmail.com
基金资助:
The work was supported by NSFC (11671193) and the Fundamental Research Funds for the Central Universities NE2015005.

EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM

Fei WU^1,2, Zejun WANG^1,2

1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China;
2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing, 211106, China

Received:2020-08-06 Revised:2021-05-18 Online:2022-02-25 Published:2022-02-24
Contact: Fei WU,E-mail:wufei003@nuaa.edu.cn E-mail:wufei003@nuaa.edu.cn
Supported by:
The work was supported by NSFC (11671193) and the Fundamental Research Funds for the Central Universities NE2015005.

摘要/Abstract

摘要： In this paper, we study the global existence of periodic solutions to an isothermal relativistic Euler system in BV space. First, we analyze some properties of the shock and rarefaction wave curves in the Riemann invariant plane. Based on these properties, we construct the approximate solutions of the isothermal relativistic Euler system with periodic initial data by using a Glimm scheme, and prove that there exists an entropy solution $V(x,t)$ which belongs to $L^{\infty}\cap {\rm BV}_{\rm loc}(\mathbb{R}\times\mathbb{R}_+)$.

关键词: isothermal relativistic Euler system, Glimm scheme, Riemann problem, BV space, periodicity

Abstract: In this paper, we study the global existence of periodic solutions to an isothermal relativistic Euler system in BV space. First, we analyze some properties of the shock and rarefaction wave curves in the Riemann invariant plane. Based on these properties, we construct the approximate solutions of the isothermal relativistic Euler system with periodic initial data by using a Glimm scheme, and prove that there exists an entropy solution $V(x,t)$ which belongs to $L^{\infty}\cap {\rm BV}_{\rm loc}(\mathbb{R}\times\mathbb{R}_+)$.

Key words: isothermal relativistic Euler system, Glimm scheme, Riemann problem, BV space, periodicity

中图分类号:

76Y05

吴菲, 王泽军. EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM[J]. 数学物理学报(英文版), 2022, 42(1): 155-171.

Fei WU, Zejun WANG. EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM[J]. Acta mathematica scientia,Series B, 2022, 42(1): 155-171.

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EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM

EXISTENCE OF PERIODIC SOLUTIONS TO AN ISOTHERMAL RELATIVISTIC EULER SYSTEM

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