Single speed solutions of the Vlasov-Poisson equations for Coulombian and Newtonian systems in nD
Results of theoretical and numerical investigations concerning the space-time evolution in nD of Coulombian systems known in Plasma Physics and Newtonian systems known in Cosmology are reported here. A generic, canonical Hamiltonian formulation is given (1) for studying single speed solutions of their Coulomb- or Jeans-Vlasov-Poisson descriptions. (2) It is shown that their equations of motion are integrable for vorticity free planar motions in nD (3) and that their characteristics are solutions of explicit non-linear ODES in general (4). Some simple examples of trajectories are illustrated and the problem of their crossing is evoked. (c) 2007 Elsevier B.V. All rights reserved.
Keywords: Coulombian and Newtonian fluids ; non-local Hamiltonian field. theory ; integrability of planar solutions ; Long-Range Interactions ; Implicit Solutions ; Eulers Equations ; 1D Systems ; Continuity ; Universe
Record created on 2010-11-30, modified on 2016-08-09