Euler-Yang-Mills equations and reduction
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.