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Dual pairs in fluid dynamics

Gay-Balmaz, François and Vizman, Cornelia (2012) Dual pairs in fluid dynamics. Annals of Global Analysis and Geometry, 41 (1). pp. 1-24. ISSN 0232-704X. doi:10.1007/s10455-011-9267-z.

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This article is a rigorous study of the dual pair structure of the ideal fluid (Phys D 7:305–323, 1983) and the dual pair structure for the n-dimensional Camassa–Holm (EPDiff) equation (The breadth of symplectic and poisson geometry: Festshrift in honor of Alan Weinstein, 2004), including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition of the momentum maps leads naturally to central extensions of diffeomorphism groups such as the group of quantomorphisms and the Ismagilov central extension.

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Additional Information:© 2011 Springer Science+Business Media B.V. Received: 2 March 2011; Accepted: 16 April 2011; Published online: 1 May 2011. We are grateful to Stefan Haller for very helpful suggestions, especially regarding Lemma 5.4. We thank Cesare Tronci for many useful and pleasant conversations about these and related matters.
Subject Keywords:Dual pair; Momentum map; Euler equation; n-Camassa-Holm equation; Central extension; Quantomorphisms
Issue or Number:1
Classification Code:Mathematics Subject Classification (2000): 53D17; 53D20; 37K65; 58D05; 58D10
Record Number:CaltechAUTHORS:20111219-091451054
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28509
Deposited By: Tony Diaz
Deposited On:20 Dec 2011 22:54
Last Modified:09 Nov 2021 16:58

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