Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 1

Geometry of nonabelian charged fluids

Pages: 5 – 19

DOI: https://dx.doi.org/10.4310/DPDE.2011.v8.n1.a2

Authors

François Gay-Balmaz (Laboratoire de Météorologie Dynamique, École Normale Supérieure, Paris, France)

Tudor S. Ratiu (Section de Mathématiques and Bernoulli Center, École Polytechnique Fédérale de Lausanne, Switzerland)

Abstract

The goal of this paper is to derive the Hamiltonian structure of polarized and magnetized Euler-Maxwell fluids by reduction of the canonical symplectic form on phase space, and to generalize the dynamics to the non- abelian case. The Hamiltonian function we propose in this case, allows us to unify and relate in a simple way the main models of nonabelian charged fluids and their Hamiltonian structures.

Keywords

reduction, Poisson brackets, nonabelian charged fluid, Yang-Mills field, Yang-Mills magnetohydrodynamics, Yang-Mills electrohydrodynamics, chromohydrodynamics

2010 Mathematics Subject Classification

37K65, 53C80, 76W05

Published 7 April 2011