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


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.


Mathematical Modeling Fluid Flow Eigenvalue Problem Industrial Mathematic Stability Problem 
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  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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