On Liapounoff's method in the theory of stability of laminar fluid flows
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In  Zhou extended some Liapounoff's theorems of the theory of stability in the case of plane laminar fluid flows. In  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  and  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.
KeywordsMathematical Modeling Fluid Flow Eigenvalue Problem Industrial Mathematic Stability Problem
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