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.
- 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.
