A dual pair for free boundary fluids

François Gay-Balmaz; Cornelia Vizman

doi:10.1142/S0219887815500681

A dual pair for free boundary fluids

François Gay-Balmaz
, Cornelia Vizman

West University in Timisoara

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a dual pair associated to the Hamiltonian geometric formulation of perfect fluids with free boundaries. This dual pair is defined on the cotangent bundle of the space of volume preserving embeddings of a manifold with boundary into a boundaryless manifold of the same dimension. The dual pair properties are rigorously verified in the infinite-dimensional Fréchet manifold setting. It provides an example of a dual pair associated to actions that are not completely mutually orthogonal.

Original language	English
Article number	1550068
Journal	International Journal of Geometric Methods in Modern Physics
Volume	12
Issue number	7
DOIs	https://doi.org/10.1142/S0219887815500681
Publication status	Published - 14 Aug 2015

Keywords

Dual pair
free boundary Euler equation
momentum map

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10.1142/S0219887815500681

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title = "A dual pair for free boundary fluids",

abstract = "We construct a dual pair associated to the Hamiltonian geometric formulation of perfect fluids with free boundaries. This dual pair is defined on the cotangent bundle of the space of volume preserving embeddings of a manifold with boundary into a boundaryless manifold of the same dimension. The dual pair properties are rigorously verified in the infinite-dimensional Fr{\'e}chet manifold setting. It provides an example of a dual pair associated to actions that are not completely mutually orthogonal.",

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AB - We construct a dual pair associated to the Hamiltonian geometric formulation of perfect fluids with free boundaries. This dual pair is defined on the cotangent bundle of the space of volume preserving embeddings of a manifold with boundary into a boundaryless manifold of the same dimension. The dual pair properties are rigorously verified in the infinite-dimensional Fréchet manifold setting. It provides an example of a dual pair associated to actions that are not completely mutually orthogonal.

KW - Dual pair

KW - free boundary Euler equation

KW - momentum map

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DO - 10.1142/S0219887815500681

M3 - Article

AN - SCOPUS:84937022640

SN - 0219-8878

VL - 12

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

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A dual pair for free boundary fluids

Abstract

Keywords

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