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A stability study of Navier-Stokes equations (III)

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Abstract

In this paper, the necessary conditions of the existence of C2 solutions in some initial problems of Navier-Stokes equations are given, and examples of instability of initial value (at t=0) problems are also given. The initial value problem of Navier-Stokes equation is one of the most fundamental problem for this equation various authors studies this problem and contributed a number of results. J. Lerav, a French professor, proved the existence of Navier-Stokes equation under certain defined initial and boundary value conditions. In this paper, with certain rigorously defined key concepts, based upon the basic theory of J. Hadamard partial differential equations1, gives a fundamental theory of instability of Navier-Stokes equations. Finally, many examples are given, proofs referring to Ref. [4].

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References

  1. Hadamard, J.,Le Problemé de Cauchy et les Épeation aux Dérivées Partielles Linéaires Hyperboliques. Hermann, Paris (1939).La Théorie des Éguations aux Dénivées Partielles. Editions Scientifiques, Pekin (1964).

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  2. Landau, L. and E. Lifchitz,Physique Théorique. Tome 6. Edition Mir Moscou (1971).

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  3. Leray, J., Essai sur le mouvement plan d'un liquide visqueux que limitent des parois.Journal Mathématique (1934).

  4. Shih, W. H.,Solutions Analytiques de Quelques Équations aux Dérivées Partielles en Mécanique des Fluides, Hermann, Paris (1992).

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  5. Shih, W. S., Une méthode élémentaire pour l'étude des équations aux dérivées partieles. Diagrammes 16, Paris (1986).C. R. Acad. Sc. Paris.303, Série 1. (1986), 439–441,304, Série I. (1987), 103–106, 187–190, 535–538.

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Authors and Affiliations

  1. Shanghai University, Shanghai

    Shi Wei-hui

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  1. Shi Wei-hui
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Communicated by Chien Wei-zang

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Wei-hui, S. A stability study of Navier-Stokes equations (III). Appl Math Mech 15, 1125–1130 (1994). https://doi.org/10.1007/BF02451983

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  • DOI: https://doi.org/10.1007/BF02451983

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