DOI: 10.7494/opmath.2007.27.2.187 ISSN: 1232-9274
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Nikolai N. Bogoliubov (Jr.), Denis L. Blackmore, Valeriy Hr. Samoylenko, Anatoliy K. PrykarpatskyA 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.