Nonlinear stability of spherical self-similar flows to the compressible Euler equations

Seung Yeal Ha, Hsiu Chuan Huang, Wen-Ching Lien

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We present the nonlinear stability of spherical self-similar flows arising from the uniform expansion of a spherical piston toward still gas. If the perturbation of the expansion speed of the piston is sufficiently small compared with the strength of the leading shock, a global weak solution of the isentropic compressible Euler system exists in the region between the spherical piston and the leading shock under the structural condition on the shock Mach number and the nondimensional piston speed. Moreover, we show that the perturbed flow tends to the corresponding self-similar flow time-asymptotically. Our analysis is based on the modified Glimm scheme.

Original languageEnglish
Pages (from-to)109-136
Number of pages28
JournalQuarterly of Applied Mathematics
Volume72
Issue number1
DOIs
Publication statusPublished - 2014 Mar 1

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Compressible Euler Equations
Euler equations
Nonlinear Stability
Pistons
Shock
Glimm Scheme
Euler System
Global Weak Solutions
Flow Time
Tend
Mach number
Perturbation
Gases

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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abstract = "We present the nonlinear stability of spherical self-similar flows arising from the uniform expansion of a spherical piston toward still gas. If the perturbation of the expansion speed of the piston is sufficiently small compared with the strength of the leading shock, a global weak solution of the isentropic compressible Euler system exists in the region between the spherical piston and the leading shock under the structural condition on the shock Mach number and the nondimensional piston speed. Moreover, we show that the perturbed flow tends to the corresponding self-similar flow time-asymptotically. Our analysis is based on the modified Glimm scheme.",
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Nonlinear stability of spherical self-similar flows to the compressible Euler equations. / Ha, Seung Yeal; Huang, Hsiu Chuan; Lien, Wen-Ching.

In: Quarterly of Applied Mathematics, Vol. 72, No. 1, 01.03.2014, p. 109-136.

Research output: Contribution to journalArticle

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