Viscous standing asymptotic states ofiIsentropic compressible flows through a nozzle

John M. Hong; Cheng Hsiung Hsu; Weishi Liu

doi:10.1007/s00205-009-0245-6

Viscous standing asymptotic states ofiIsentropic compressible flows through a nozzle

John M. Hong, Cheng Hsiung Hsu, Weishi Liu

Department of Mathematics

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

15 Scopus citations

Abstract

In this work we consider a viscous regularization of a well-known one-dimensional model for isentropic viscous compressible flows through a nozzle. For the existence and multiplicity of standing asymptotic states for a certain type of ducts, a complete analysis in a framework of dynamical systems is provided. As an application of the geometric singular perturbation theory, we show that all standing asymptotic states admit viscous profiles.

Original language	English
Pages (from-to)	575-597
Number of pages	23
Journal	Archive for Rational Mechanics and Analysis
Volume	196
Issue number	2
DOIs	https://doi.org/10.1007/s00205-009-0245-6
State	Published - May 2010

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abstract = "In this work we consider a viscous regularization of a well-known one-dimensional model for isentropic viscous compressible flows through a nozzle. For the existence and multiplicity of standing asymptotic states for a certain type of ducts, a complete analysis in a framework of dynamical systems is provided. As an application of the geometric singular perturbation theory, we show that all standing asymptotic states admit viscous profiles.",

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

note = "Funding Information: Partially supported by NSF of USA grants DMS-0406998, DMS-0807327 and by the University of Kansas GRF-2301158. Funding Information: Partially supported by the National Science Council, NCTS of Taiwan and CMTP of NCU. Funding Information: Partially supported by the National Science Council of Taiwan and CMTP of NCU. ",

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AU - Hsu, Cheng Hsiung

AU - Liu, Weishi

N1 - Funding Information: Partially supported by NSF of USA grants DMS-0406998, DMS-0807327 and by the University of Kansas GRF-2301158. Funding Information: Partially supported by the National Science Council, NCTS of Taiwan and CMTP of NCU. Funding Information: Partially supported by the National Science Council of Taiwan and CMTP of NCU.

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N2 - In this work we consider a viscous regularization of a well-known one-dimensional model for isentropic viscous compressible flows through a nozzle. For the existence and multiplicity of standing asymptotic states for a certain type of ducts, a complete analysis in a framework of dynamical systems is provided. As an application of the geometric singular perturbation theory, we show that all standing asymptotic states admit viscous profiles.

AB - In this work we consider a viscous regularization of a well-known one-dimensional model for isentropic viscous compressible flows through a nozzle. For the existence and multiplicity of standing asymptotic states for a certain type of ducts, a complete analysis in a framework of dynamical systems is provided. As an application of the geometric singular perturbation theory, we show that all standing asymptotic states admit viscous profiles.

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Viscous standing asymptotic states ofiIsentropic compressible flows through a nozzle

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