Uniqueness of generalized elements of best approximation

Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

“…For the case with electrostatic Coulomb interaction we find the eigenfrequencies of longitudinal plasma waves as divergences of the correlation function for small wave vectors. Also we find that our result is equivalent to the solution of the Vlasov equation for small perturbations around thermal equilibrium [20]. The Vlasov equation is the kinetic theory of collisionless plasmas, i.e.…”

“…This result can now be related to kinetic theory where the Vlasov equation is used [20]. Then charged particles in a neutralizing background are considered.…”

“…This equation is like the Boltzmann equation but the collision term that represents direct two-particle collisions is neglected. Instead the pair interaction enters via the a-term as an external force from an average over many neighboring particles [20].…”

Gravitational instability of a nonrotating galaxy

“…Whether we are considering a star or a dust particle in the galaxy does not matter. Following standard treatment in accelerator physics, evolution of is described by the Vlasov equation [4],…”

Weak Plasma Turbulence Theory and Some Other Items of Plasma Kinetics

“…The existing machinery for the kinetic description of plasma collective motions is based on the Vlasov equation (Vlasov 1945). It is worth noting that the Vlasov equation coincides, in its form, with the Klimontovich-Dupree equation (see Klimontovich 1967 andDupree 1963)-they differ only in the assumptions made about the solution to this equation.…”