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

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Abstract

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.

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REFERENCES

  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.

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  2. Nelineinye sistemy gidrodinamicheskogo tipa (Nonlinear Systems of Hydrodinamical Type), Obukhov, A.M., Ed., Moscow: Nauka, 1974.

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  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].

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  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].

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Authors and Affiliations

  1. Smidt United Institute of Physics of Earth, RAS, Moscow

    E. I. Dinaburg

  2. International Institute of Theory of Earthquake Prediction and Mathematical Geophysics, RAS, Moscow

    E. I. Dinaburg

  3. Mathematical Department, Princeton University. Landau Institute of Theoretical Physics, RAS, Moscow

    Ya. G. Sinai

Authors
  1. E. I. Dinaburg
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  2. Ya. G. Sinai
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Dinaburg, E.I., Sinai, Y.G. Existence and Uniqueness of Solutions of a Quasilinear Approximation of the 3D Navier–Stokes System. Problems of Information Transmission 39, 47–50 (2003). https://doi.org/10.1023/A:1023678431203

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  • DOI: https://doi.org/10.1023/A:1023678431203

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