Applied Mathematics and Mechanics

, Volume 15, Issue 12, pp 1125–1130 | Cite as

A stability study of Navier-Stokes equations (III)

  • Shi Wei-hui


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].

Key words

Ehresmann space basic equation Cauchy problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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).Google Scholar
  2. [2]
    Landau, L. and E. Lifchitz,Physique Théorique. Tome 6. Edition Mir Moscou (1971).Google Scholar
  3. [3]
    Leray, J., Essai sur le mouvement plan d'un liquide visqueux que limitent des parois.Journal Mathématique (1934).Google Scholar
  4. [4]
    Shih, W. H.,Solutions Analytiques de Quelques Équations aux Dérivées Partielles en Mécanique des Fluides, Hermann, Paris (1992).Google Scholar
  5. [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.Google Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Shi Wei-hui
    • 1
  1. 1.Shanghai UniversityShanghai

Personalised recommendations