Opuscula Mathematica

Opuscula Math.
, no. 2
 (), 187-195
Opuscula Mathematica

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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