Vlasov and Liouville-type equations and its microscopic and hydrodynamic consequences
Abstract:
Derivations of Vlasov-Maxwell and Vlasov-Poisson-Poisson equations from Lagrangians of classical electrodynamics are considered. Equations of electromagnetic hydrodynamics and electrostatics with gravitation are brought out of them by means of hydrodynamic substitution. Advantages of S.K. Godunov twice divergent form of EMHD are discussed. Possibility of the simplest derivation of the classical equation of Hamilto-Jacobi method from Liouville's one is shown, and also analog of this procedure both Vlasov equation, and for non-Hamiltonian case.
