Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids

Abstract

The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are 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 a non-canonical Poisson bracket associated to these equations.