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.