Opuscula Math. 27, no. 2 (2007), 187-195
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.
About the authors ▼
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
About the article ▼
Received: 2006-01-31.
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,
http://dx.doi.org/10.7494/OpMath.2007.27.2.187.
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