Euler-Yang-Mills equations and reduction
Abstract:
The Lagrangian and Hamiltonian structures for an ideal
gauge-charged fluid is determined. Using a Kaluza-Klein
point of view, the equations of motion are obtained by
Lagrangian and Poisson reductions associated to the
automorphism group of a principal bundle. As a consequence
of the Lagrangian approach, a Kelvin-Noether theorem is
obtained. The Hamiltonian formulation determines the
non-canonical Poisson bracket associated to these
equations.