Hamilton-Pontryagin principle for incompressible ideal fluids

Hiroaki Yoshimura; François Gay-Balmaz

doi:10.1063/1.3652002

Hamilton-Pontryagin principle for incompressible ideal fluids

Hiroaki Yoshimura, François Gay-Balmaz

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

We develop the Hamilton-Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler-Poincaré equations with advective parameters. Then, we derive the reduced Hamilton-Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton-Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler-Poincaré equations.

Original language	English
Title of host publication	Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI
Pages	645-647
Number of pages	3
DOIs	https://doi.org/10.1063/1.3652002
Publication status	Published - 2011 Jan 1
Event	Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI - Guangzhou, China Duration: 2011 Jun 30 → 2011 Jul 3

Publication series

Name	AIP Conference Proceedings
Volume	1376
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI
Country	China
City	Guangzhou
Period	11/6/30 → 11/7/3

Keywords

Advective Parameters
Hamilton-Pontryagin Principle
Implicit Euler-Poincaré Equations

ASJC Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1063/1.3652002

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Yoshimura, H., & Gay-Balmaz, F. (2011). Hamilton-Pontryagin principle for incompressible ideal fluids. In Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI (pp. 645-647). (AIP Conference Proceedings; Vol. 1376). https://doi.org/10.1063/1.3652002

Hamilton-Pontryagin principle for incompressible ideal fluids. / Yoshimura, Hiroaki; Gay-Balmaz, François.

Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI. 2011. p. 645-647 (AIP Conference Proceedings; Vol. 1376).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yoshimura, H & Gay-Balmaz, F 2011, Hamilton-Pontryagin principle for incompressible ideal fluids. in Recent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI. AIP Conference Proceedings, vol. 1376, pp. 645-647, Proceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI, Guangzhou, China, 11/6/30. https://doi.org/10.1063/1.3652002

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