Reductions of fluid and kinetic equations using Dirac'stheory of constrained Hamiltonian systems

PDE Seminar
Tuesday, August 20, 2013 - 15:00
1 hour (actually 50 minutes)
Center for Theoretical Physics, Univ. Aix-Marseille
Dirac'stheory of constrained Hamiltonian systems allows for reductions of the dynamics in a Hamiltonian framework. Starting from an appropriate set of constraints on the dynamics, Dirac'stheory provides a bracket for the reduced dynamics. After a brief introduction of Dirac'stheory, I will illustrate the approach on ideal magnetohydrodynamics and Vlasov-Maxwell equations. Finally I will discuss the conditions under which the Dirac bracket can be constructed and is a Poisson bracket.