Monday, November 7, 2011 - 11:00
1 hour (actually 50 minutes)
The Vlasov-Poisson and Vlasov-Maxwell equations possess variousvariational formulations1 or action principles, as they are generallytermed by physicists. I will discuss a particular variational principlethat is based on a Hamiltonian-Jacobi formulation of Vlasov theory,a formulation that is not widely known. I will show how this formu-lation can be reduced for describing the Vlasov-Poisson system. Theresulting system is of Hamilton-Jacobi form, but with nonlinear globalcoupling to the Poisson equation. A description of phase (function)space geometry will be given and comments about Hamilton-Jacobipde methods and weak KAM will be made.Supported by the US Department of Energy Contract No. DE-FG03-96ER-54346.H. Ye and P. J. Morrison Phys. Fluids 4B 771 (1992).D. Prsch, Z. Naturforsch. 39a, 1 (1984); D. Prsch and P. J. Morrison, Phys. Rev.32A, 1714 (1985).