Opuscula Math. 27, no. 2 (2007), 187-195

Opuscula Mathematica

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

Nikolai N. Bogoliubov (Jr.)
Denis L. Blackmore
Valeriy Hr. Samoylenko
Anatoliy K. Prykarpatsky

Abstract. A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

Keywords: kinetic Boltzmann-Vlasov equations, hydrodynamic model, Hamiltonian systems, invariants, dynamical equivalence.

Mathematics Subject Classification: 58F08, 70H35, 34B15.

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  • Nikolai N. Bogoliubov (Jr.)
  • V. A. Steklov Mathematical Institute of RAN, Moscow, Russia
  • Denis L. Blackmore
  • Department of Mathematical Sciences at the NJIT, NJ, 07102 Newark, USA
  • Valeriy Hr. Samoylenko
  • Dept. of Mechanics and Mathematics at the Shevchenko National University, Kyiv, 00617, Ukraine
  • Anatoliy K. Prykarpatsky
  • AGH University of Science and Technology, Faculty of Applied Mathematics, Cracow 30-059, Poland
  • Received: 2006-01-31.
Opuscula Mathematica - cover

Cite this article as:
Nikolai N. Bogoliubov (Jr.), Denis L. Blackmore, Valeriy Hr. Samoylenko, Anatoliy K. Prykarpatsky, On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity, Opuscula Math. 27, no. 2 (2007), 187-195

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