THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

doi:10.1007/s10473-022-0413-4

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1519-1535.doi: 10.1007/s10473-022-0413-4

THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

刘思杰, 盛万成

Department of Mathematics, Shanghai University, Shanghai, 200444, China

收稿日期:2021-02-02 出版日期:2022-08-25 发布日期:2022-08-23
通讯作者: Wancheng SHENG,E-mail:mathwcsheng@shu.edu.cn E-mail:mathwcsheng@shu.edu.cn
基金资助:
Supported by NSFC (12171305).

THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

Sijie LIU, Wancheng SHENG

Department of Mathematics, Shanghai University, Shanghai, 200444, China

Received:2021-02-02 Online:2022-08-25 Published:2022-08-23
Contact: Wancheng SHENG,E-mail:mathwcsheng@shu.edu.cn E-mail:mathwcsheng@shu.edu.cn
Supported by:
Supported by NSFC (12171305).

摘要/Abstract

摘要： This paper is concerned with the pressureless Euler equations with viscous and flux perturbations. The existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is obtained. We show the stability of the delta wave of the pressureless Euler equations to the perturbations; that is, the limit solution of the pressureless Euler equations with viscous and flux perturbations is the delta wave solution of the pressureless Euler equations as the viscous and flux perturbation simultaneously vanish in the case $u_->u_+$.

关键词: Pressureless Euler equations, stability of the delta wave, viscous perturbation and flux perturbation

Abstract: This paper is concerned with the pressureless Euler equations with viscous and flux perturbations. The existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is obtained. We show the stability of the delta wave of the pressureless Euler equations to the perturbations; that is, the limit solution of the pressureless Euler equations with viscous and flux perturbations is the delta wave solution of the pressureless Euler equations as the viscous and flux perturbation simultaneously vanish in the case $u_->u_+$.

Key words: Pressureless Euler equations, stability of the delta wave, viscous perturbation and flux perturbation

中图分类号:

35L65

刘思杰, 盛万成. THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS[J]. 数学物理学报(英文版), 2022, 42(4): 1519-1535.

Sijie LIU, Wancheng SHENG. THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1519-1535.

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THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

THE STABILITY OF THE DELTA WAVE TO PRESSURELESS EULER EQUATIONS WITH VISCOUS AND FLUX PERTURBATIONS

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