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Euler and Navier–Stokes Equations as Self-Consistent Fields

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Abstract

New kinetic equations are proposed from which the incompressible Euler and Navier–Stokes equations are derived by making an exact substitution. A class of exact solutions of the Navier–Stokes equation and the form of singularities for a gradient catastrophe are obtained.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia

    V. V. Vedenyapin

  2. RUDN University, Moscow, 117198, Russia

    V. V. Vedenyapin

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    A. A. Andreeva & V. V. Vorobyeva

Authors
  1. V. V. Vedenyapin
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  2. A. A. Andreeva
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  3. V. V. Vorobyeva
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Corresponding author

Correspondence to V. V. Vedenyapin.

Additional information

Original Russian Text © V.V. Vedenyapin, A.A. Andreeva, V.V. Vorobyeva, 2018, published in Doklady Akademii Nauk, 2018, Vol. 480, No. 4, pp. 405–407.

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Vedenyapin, V.V., Andreeva, A.A. & Vorobyeva, V.V. Euler and Navier–Stokes Equations as Self-Consistent Fields. Dokl. Math. 97, 283–285 (2018). https://doi.org/10.1134/S1064562418030171

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  • DOI: https://doi.org/10.1134/S1064562418030171

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