On kinetic two component Boltzmann equations and related hydrodynamic two liquid flows
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
There is discussed 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. We show that they have a natural connection with the
nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional
particle flows with a pointwise interaction potential between particles. A
new type of hydrodynamic two-component Benney equations is constructed,
their Hamiltonian structure is found. The question about the existence of
the related Lax type representation for the two-component case is still
remaining to be open.