Shi Wei-hui. A Stability Study of Navier-Stokes Equations(Ⅲ)[J]. Applied Mathematics and Mechanics, 1994, 15(12): 1067-1073.
Citation: Shi Wei-hui. A Stability Study of Navier-Stokes Equations(Ⅲ)[J]. Applied Mathematics and Mechanics, 1994, 15(12): 1067-1073.

A Stability Study of Navier-Stokes Equations(Ⅲ)

  • Received Date: 1994-01-20
  • Publish Date: 1994-12-15
  • In this paper, the necessary conditions of the existence of C2 solution. in someinitial problems of Navier-Stokes equations are given. and examples of instability ofinitial 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 equationvarious authors studies this problem and contributed a number of results.J.Leray.a French professor, proved the existence of Navier-Stokes equation under certain definedinitial and boundary value conditions.In this paper,with certain rigorously defined key concepts,based upon the basic theory of J.Hadmard partial differential equanous[1], gives a fundamental theory of instability of Navier-Stokes equations.Finally,many examples are given,proofs referring to reference.[4].
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  • [1]
    Hadamard, J.,Le Probleme de Cauchy et les Epeaiion aux Derives Partielles Lineaires Hyperboliques, Harmann, Paris(1939), Lo Theorie des Equations aux Derivees Partielles, Editions Scientifiques, Pekin(1964).
    [2]
    Landau, L, and E, Lifcuiez, Physique Thceorique, Tome 6, Edition Mir Moscou(1971).
    [3]
    Leray,J.Essai sur le mouvement plan d'un liquide visqucuz que limitent des parois, Journal Mathematique(1934).
    [4]
    Shih,W.H.Solutions Anaiytiques de Quelques Equations aux Derivees Portiellss en Mecanique des Fluides, Hermann, Paris(1992).
    [5]
    Shih, W, S,,Une methode elemcntaire pour I'etude des equatioas aux derivees partielles, Diagrammes 16, Paris(1986), C, R.Acad, Sc, Paris, 303, Serie I.(1986), 439-441, 304 Serie I (1987), 103-106, 187-190, 535-538.
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