| ON LIAPOUNOFF’S METHOD IN THE THEORY OF STABILITY OF LAMINAR FLUID FLOWS |
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| 引用本文： | 周恒,李骊. ON LIAPOUNOFF’S METHOD IN THE THEORY OF STABILITY OF LAMINAR FLUID FLOWS[J]. 应用数学和力学(英文版), 1983, 4(4): 481-492. DOI: 10.1007/BF01874662 |
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| 作者姓名： | 周恒 李骊 |
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| 作者单位： | Tianjin University，Tianjin，Tianjin University，Tianjin |
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| 摘 要： | 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 pro-blem of plane laminar fluid flows for sufficiently small initial disturbance.
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| 收稿时间： | 1982-07-25 |
On Liapounoff's method in the theory of stability of laminar fluid flows |
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| Zhou Heng,Li Li. On Liapounoff's method in the theory of stability of laminar fluid flows[J]. Applied Mathematics and Mechanics(English Edition), 1983, 4(4): 481-492. DOI: 10.1007/BF01874662 |
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| Authors: | Zhou Heng Li Li |
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| Affiliation: | Tianjin University, Tianjin |
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| 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. |
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