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Mosc. Math. J., 2001, Volume 1, Number 3, Pages 381–388 (Mi mmj26)  

This article is cited in 13 scientific papers (total in 13 papers)

A quasilinear approximation for the three-dimensional Navier–Stokes system

E. I. Dinaburgab, Ya. G. Sinaicd

a Schmidt United Institute of Physics of the Earth, Russian Academy of Scienses
b International Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
c L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
d Princeton University, Department of Mathematics

Abstract: In this paper a modification of the 3-dimensional Navier–Stokes system which defines some system of quasilinear equations in Fourier space is considered. Properties of the obtained system and its finite-dimensional approximations are studied.

Key words and phrases: Three-dimensional Navier–Stokes system, quasilinear system, characteristics.

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MSC: 76D05
Received: July 6, 2001; in revised form September 24, 2001
Language: English

Citation: E. I. Dinaburg, Ya. G. Sinai, “A quasilinear approximation for the three-dimensional Navier–Stokes system”, Mosc. Math. J., 1:3 (2001), 381–388

Citation in format AMSBIB
\by E.~I.~Dinaburg, Ya.~G.~Sinai
\paper A quasilinear approximation for the three-dimensional Navier--Stokes system
\jour Mosc. Math.~J.
\yr 2001
\vol 1
\issue 3
\pages 381--388

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    This publication is cited in the following articles:
    1. Sinai Y.G., “What, in my opinion, David Ruelle should do in the coming years?”, Journal of Statistical Physics, 108:5–6 (2002), 729–732  crossref  mathscinet  zmath  isi
    2. Dinaburg E.I., “New finite-dimensional approximations of the 3D Navier–Stokes system”, Doklady Mathematics, 65:2 (2002), 175–179  mathnet  mathscinet  zmath  isi
    3. E. I. Dinaburg, Ya. G. Sinai, “Existence and Uniqueness of Solutions of a Quasilinear Approximation for the Three-Dimensional Navier–Stokes System”, Problems Inform. Transmission, 39:1 (2003), 47–50  mathnet  crossref  mathscinet  zmath
    4. Dinaburg E.I., Sinai Y.G., “On some approximation of the 3D Euler system”, Ergodic Theory and Dynamical Systems, 24:5 (2004), 1443–1450  crossref  mathscinet  zmath  isi
    5. Sinai Y.G., “Mathematical hydrodynamics”, Russian Journal of Mathematical Physics, 11:3 (2004), 355–358  mathscinet  zmath  isi
    6. Friedlander S., Pavlovic N., “Blowup in a three-dimensional vector model for the Euler equations”, Communications on Pure and Applied Mathematics, 57:6 (2004), 705–725  crossref  mathscinet  zmath  isi
    7. Gledzer E.B., “Dissipation and intermittency of turbulence in the framework of hydrodynamic approximations”, Izvestiya Atmospheric and Oceanic Physics, 41:6 (2005), 667–683  mathscinet  isi
    8. Kiselev A., Zlatos A., “On discrete models of the Euler equation”, International Mathematics Research Notices, 2005, no. 38, 2315–2339  crossref  mathscinet  zmath  isi  elib
    9. Waleffe F., “On some dyadic models of the Euler equations”, Proceedings of the American Mathematical Society, 134:10 (2006), 2913–2922  crossref  mathscinet  zmath  isi
    10. Cheskidov A., Friedlander S., Pavlovic N., “Inviscid dyadic model of turbulence: The fixed point and Onsager's conjecture”, Journal of Mathematical Physics, 48:6 (2007), 065503  crossref  mathscinet  adsnasa  isi
    11. Cheskidov A., “Blow-up in finite time for the dyadic model of the Navier–Stokes equations”, Transactions of the American Mathematical Society, 360:10 (2008), 5101–5120  crossref  mathscinet  zmath  isi
    12. Cheskidov A., Friedlander S., Pavlovic N., “An Inviscid Dyadic Model of Turbulence: the Global Attractor”, Discrete and Continuous Dynamical Systems, 26:3 (2010), 781–794  crossref  mathscinet  zmath  isi
    13. Jeong I.-J., Li D., “a Blow-Up Result For Dyadic Models of the Euler Equations”, Commun. Math. Phys., 337:2 (2015), 1027–1034  crossref  mathscinet  zmath  isi
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