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

  • Weishi Liu
  • Myunghyun Oh
Chapter
Part of the Fields Institute Communications book series (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.

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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