Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area

John M. Hong; Cheng Hsiung Hsu; Ying Chieh Lin; Weishi Liu

doi:10.1016/j.jde.2012.11.011

Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area

John M. Hong, Cheng Hsiung Hsu, Ying Chieh Lin, Weishi Liu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this work we consider the linear stability of the sub-to-super inviscid transonic stationary wave of a one-dimensional model of isentropic compressible flows through a nozzle of varying area. This sub-to-super inviscid transonic stationary wave is newly founded by the authors using the geometric singular perturbation theory. The main result of this work is to show that the sub-to-super inviscid transonic stationary wave is physically relevant in the sense that it is L^∞ linearly stable on any bounded space interval as long as its velocity is greater than 1/2 of the sound speed.

Original language	English
Pages (from-to)	1957-1976
Number of pages	20
Journal	Journal of Differential Equations
Volume	254
Issue number	4
DOIs	https://doi.org/10.1016/j.jde.2012.11.011
State	Published - 15 Feb 2013

Keywords

Geometric singular perturbation theory
Sobolev's embedding theorem
Sub-to-super inviscid transonic stationary wave

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10.1016/j.jde.2012.11.011

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title = "Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area",

abstract = "In this work we consider the linear stability of the sub-to-super inviscid transonic stationary wave of a one-dimensional model of isentropic compressible flows through a nozzle of varying area. This sub-to-super inviscid transonic stationary wave is newly founded by the authors using the geometric singular perturbation theory. The main result of this work is to show that the sub-to-super inviscid transonic stationary wave is physically relevant in the sense that it is L∞ linearly stable on any bounded space interval as long as its velocity is greater than 1/2 of the sound speed.",

keywords = "Geometric singular perturbation theory, Sobolev's embedding theorem, Sub-to-super inviscid transonic stationary wave",

author = "Hong, {John M.} and Hsu, {Cheng Hsiung} and Lin, {Ying Chieh} and Weishi Liu",

note = "Funding Information: E-mail addresses: [email protected] (J.M. Hong), [email protected] (C.-H. Hsu), [email protected] (Y.-C. Lin), [email protected] (W. Liu). 1 Partially supported by National Science Council of Taiwan. 2 Partially supported by National Science Council and NCTS of Taiwan. 3 Partially supported by National Science Foundation of USA Grant DMS-0807327 and University of Kansas GRF 2301264-003.",

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T1 - Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area

AU - Hong, John M.

AU - Hsu, Cheng Hsiung

AU - Lin, Ying Chieh

AU - Liu, Weishi

N1 - Funding Information: E-mail addresses: [email protected] (J.M. Hong), [email protected] (C.-H. Hsu), [email protected] (Y.-C. Lin), [email protected] (W. Liu). 1 Partially supported by National Science Council of Taiwan. 2 Partially supported by National Science Council and NCTS of Taiwan. 3 Partially supported by National Science Foundation of USA Grant DMS-0807327 and University of Kansas GRF 2301264-003.

PY - 2013/2/15

Y1 - 2013/2/15

N2 - In this work we consider the linear stability of the sub-to-super inviscid transonic stationary wave of a one-dimensional model of isentropic compressible flows through a nozzle of varying area. This sub-to-super inviscid transonic stationary wave is newly founded by the authors using the geometric singular perturbation theory. The main result of this work is to show that the sub-to-super inviscid transonic stationary wave is physically relevant in the sense that it is L∞ linearly stable on any bounded space interval as long as its velocity is greater than 1/2 of the sound speed.

AB - In this work we consider the linear stability of the sub-to-super inviscid transonic stationary wave of a one-dimensional model of isentropic compressible flows through a nozzle of varying area. This sub-to-super inviscid transonic stationary wave is newly founded by the authors using the geometric singular perturbation theory. The main result of this work is to show that the sub-to-super inviscid transonic stationary wave is physically relevant in the sense that it is L∞ linearly stable on any bounded space interval as long as its velocity is greater than 1/2 of the sound speed.

KW - Geometric singular perturbation theory

KW - Sobolev's embedding theorem

KW - Sub-to-super inviscid transonic stationary wave

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U2 - 10.1016/j.jde.2012.11.011

DO - 10.1016/j.jde.2012.11.011

M3 - 期刊論文

AN - SCOPUS:84871408778

SN - 0022-0396

VL - 254

SP - 1957

EP - 1976

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area

Abstract

Keywords

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