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Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface

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Abstract

We establish the complete integrability of a nonlinear dynamical system associated with the hydrodynamic Navier-Stokes equations for the flow of an ideal two-dimensional liquid with a free surface over the horizontal bottom. We show that this dynamical system is naturally connected with the nonlinear kinetic Boltzmann-Vlasov equation for a one-dimensional flow of particles with a point potential of interaction between particles.

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Authors and Affiliations

  1. Institute of mathematics, Ukrainian Academy of Sciences, Kiev

    V. G. Samoilenko

  2. Samarkand University, USSR

    U. S. Suyarov

Authors
  1. V. G. Samoilenko
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  2. U. S. Suyarov
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 86–90, January, 1993.

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Samoilenko, V.G., Suyarov, U.S. Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface. Ukr Math J 45, 94–99 (1993). https://doi.org/10.1007/BF01062042

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  • DOI: https://doi.org/10.1007/BF01062042

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