Journal of Symplectic Geometry

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

Francois Gay-Balmaz and Tudor S. Ratiu

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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.

Article information

Source
J. Symplectic Geom., Volume 6, Number 2 (2008), 189-237.

Dates
First available in Project Euclid: 27 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1219866512

Mathematical Reviews number (MathSciNet)
MR2434440

Zentralblatt MATH identifier
1149.70015

Citation

Gay-Balmaz, Francois; Ratiu, Tudor S. Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids. J. Symplectic Geom. 6 (2008), no. 2, 189--237. https://projecteuclid.org/euclid.jsg/1219866512


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