Hamilton-Pontryagin principle for incompressible ideal fluids

Hiroaki Yoshimura, François Gay-Balmaz

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationRecent Progresses in Fluid Dynamics Research - Proceedings of the Sixth International Conference on Fluid Mechanics, ICFM VI
Pages645-647
Number of pages3
DOIs
Publication statusPublished - 2011 Jan 1
EventProceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI - Guangzhou, China
Duration: 2011 Jun 302011 Jul 3

Publication series

NameAIP Conference Proceedings
Volume1376
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceProceedings of the 6th International Conference on Fluid Mechanics: Recent Progresses in Fluid Dynamics Research, ICFM VI
CountryChina
CityGuangzhou
Period11/6/3011/7/3

Keywords

  • Advective Parameters
  • Hamilton-Pontryagin Principle
  • Implicit Euler-Poincaré Equations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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  • Cite this

    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