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Journal of Mathematical Fluid Mechanics

, Volume 17, Issue 1, pp 129–143 | Cite as

Instability of Plane Poiseuille Flow in Viscous Compressible Gas

  • Yoshiyuki KageiEmail author
  • Takaaki Nishida
Article

Abstract

Instability of plane Poiseuille flow in viscous compressible gas is investigated. A condition for the Reynolds and Mach numbers is given in order for plane Poiseuille flow to be unstable. It turns out that plane Poiseuille flow is unstable for Reynolds numbers much less than the critical Reynolds number for the incompressible flow when the Mach number is suitably large. It is proved by the analytic perturbation theory that the linearized operator around plane Poiseuille flow has eigenvalues with positive real part when the instability condition for the Reynolds and Mach numbers is satisfied.

Keywords

Compressible Navier-Stokes equation Poiseuille flow instability 

Mathematics Subject Classification

35Q30 76N15 

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References

  1. 1.
    Iooss G., Padula M.: Structure of the linearized problem for compressible parallel fluid flows. Ann. Univ. Ferrara, Sez. VII 43, 157–171 (1998)MathSciNetGoogle Scholar
  2. 2.
    Kagei Y.: Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow. Arch. Rational Mech. Anal. 205, 585–650 (2012)CrossRefADSzbMATHMathSciNetGoogle Scholar
  3. 3.
    Kagei, Y., Nagafuchi, Y., Sudo, T.: Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Poiseuille type flow. J. Math-for-Ind. 2A (2010), 39–56. Correction to “Decay estimates on solutions of the linearized compressible Navier-Stokes equation around a Poiseuille type flow” in J. Math-for-Ind. 2A (2010), pp. 39–56 J. Math-for-Ind. 2B (2010), 235Google Scholar
  4. 4.
    Kato T.: Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, Heidelberg, New York (1980)zbMATHGoogle Scholar
  5. 5.
    Reed M., Simon B.: Methods of Modern Mathematical Physics IV. Academic Press, London (1979)Google Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Department of Applied Complex SystemKyoto UniversityKyotoJapan

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