Problems of Information Transmission

, Volume 39, Issue 1, pp 47–50 | Cite as

Existence and Uniqueness of Solutions of a Quasilinear Approximation of the 3D Navier–Stokes System

  • E. I. Dinaburg
  • Ya. G. Sinai


For the quasilinear approximation of the 3D Navier–Stokes system proposed earlier by the authors in [1], some conditions of solution regularity are considered and the theorem on existence and uniqueness of the Cauchy problem for some class of initial data is proved.


Initial Data Cauchy Problem System Theory Stokes System Solution Regularity 
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  1. 1.
    Dinaburg, E.I. and Sinai, Ya.G., A Quasi-Linear Approximation of Three-Dimensional Navier–Stokes System, Moscow Math. J., 2001, vol. 1, no. 3, pp. 381–388.Google Scholar
  2. 2.
    Nelineinye sistemy gidrodinamicheskogo tipa (Nonlinear Systems of Hydrodinamical Type), Obukhov, A.M., Ed., Moscow: Nauka, 1974.Google Scholar
  3. 3.
    E, W. and Sinai, Ya.G., Recent Results on Mathematical and Statistical Hydrodinamics, Usp. Mat. Nauk, 2000, vol. 55, no. 4, pp. 25–59 [Russian Math. Surveys (Engl. Transl.), 2000, vol. 55, no. 4, pp. 635–666].Google Scholar
  4. 4.
    Dinaburg, E.I., New Finite-Dimensional Approximations of the 3D Navier–Stokes System, Dokl. Ross. Akad. Nauk, 2002, vol. 383, pp. 151–155 [Dokl. Math. (Engl. Transl.), 2002, vol. 65, no. 2, pp. 175–179].Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2003

Authors and Affiliations

  • E. I. Dinaburg
    • 1
    • 2
  • Ya. G. Sinai
    • 3
  1. 1.Smidt United Institute of Physics of Earth, RASMoscow
  2. 2.International Institute of Theory of Earthquake Prediction and Mathematical Geophysics, RASMoscow
  3. 3.Mathematical DepartmentPrinceton University. Landau Institute of Theoretical Physics, RASMoscow

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