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

doi:10.1007/s10473-022-0413-4

Abstract

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

CLC Number:

35L65

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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