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 | |
| 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 |
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Keywords
- Advective Parameters
- Hamilton-Pontryagin Principle
- Implicit Euler-Poincaré Equations
ASJC Scopus subject areas
- Physics and Astronomy(all)
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