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Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozzle

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Infinite Dimensional Dynamical Systems

Part of the book series: Fields Institute Communications ((FIC,volume 64))

Abstract

In this work, we examine the stability of stationary non-transonic waves for viscous isentropic compressible flows through a nozzle with varying cross-section areas. The main result in this paper is, for small viscous strength, stationary supersonic waves with sufficiently low density are spectrally unstable; more precisely, we will establish the existence of positive eigenvalues for the linearization along such waves. The result is achieved via a center manifold reduction of the eigenvalue problem. The reduced eigenvalue problem is then studied in the framework of the Sturm–Liouville Theory.

Mathematics Subject Classification (2010): Primary 35B35; Secondary 76N17, 35L65

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Acknowledgements

Weishi Liu was partially supported by NSF grant DMS-0807327 and KU GRF 2301264-003. Myunghyun Oh was partially supported by NSF grant DMS-0708554.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Weishi Liu & Myunghyun Oh

Authors
  1. Weishi Liu
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  2. Myunghyun Oh
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Correspondence to Weishi Liu .

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Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, USA

    John Mallet-Paret

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jianhong Wu  & Huaiping Zhu  & 

  3. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA

    Yingfei Yi

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Liu, W., Oh, M. (2013). Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozzle. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_6

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