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

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

4 引文斯高帕斯（Scopus）

摘要

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.

原文	???core.languages.en_GB???
頁（從 - 到）	1957-1976
頁數	20
期刊	Journal of Differential Equations
卷	254
發行號	4
DOIs	https://doi.org/10.1016/j.jde.2012.11.011
出版狀態	已出版 - 15 2月 2013

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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

UR - https://www.scopus.com/pages/publications/84871408778

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

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