Applied Mathematics and Mechanics

, Volume 4, Issue 4, pp 481–492 | Cite as

On Liapounoff's method in the theory of stability of laminar fluid flows

  • Zhou Heng
  • Li Li
Article
  • 19 Downloads

Abstract

In [1] Zhou extended some Liapounoff's theorems of the theory of stability in the case of plane laminar fluid flows. In [2] Zhou and Li investigated the eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation, and obtained some new results. In this paper, based on the results of [1] and [2] we shall prove: (1) For the linearized problem the definition of stability according to the eigenvalues of Orr-Sommerfeld equation and that according to the perturbation energy are equivalent; (2) The method of linearization is admissible for the stability problem of plane laminar fluid flows for sufficiently small initial disturbance.

Keywords

Mathematical Modeling Fluid Flow Eigenvalue Problem Industrial Mathematic Stability Problem 

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References

  1. [1]
    Zhou Heng,The extension of some Liapounoff's theorems of the theory of stability in the case of continuum mechanics, Acta Mechanica Sinica, Vol. 8, No. 1 (1965). (in Chinese)Google Scholar
  2. [2]
    Zhou Heng and Li Li,The eigenvalue problem and expansion theorem associated with Orr-Sommerfeld equation, Appl. Meth. and Mech. English edit. Vol. 2, No. 3 (1981).Google Scholar
  3. [3]
    Lin, C.C.,Theory of Hydrodynamic Stability, Cambridge, (1955).Google Scholar
  4. [4]
    Naimark, M.A.,Linear differential opertor, GITTL, Moscow, (1954) (in Russian)Google Scholar

Copyright information

© Hust Press 1983

Authors and Affiliations

  • Zhou Heng
    • 1
  • Li Li
    • 1
  1. 1.Tianjin UniversityTianjin

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