Annals of Global Analysis and Geometry

, Volume 41, Issue 1, pp 1–24 | Cite as

Dual pairs in fluid dynamics

  • François Gay-Balmaz
  • Cornelia VizmanEmail author
Original Paper


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.


Dual pair Momentum map Euler equation n-Camassa–Holm equation Central extension Quantomorphisms 

Mathematics Subject Classification (2000)

53D17 53D20 37K65 58D05 58D10 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Control and Dynamical SystemsCalifornia Institute of Technology 107-81PasadenaUSA
  2. 2.LMD, Ecole Normale Supérieure/CNRSParisFrance
  3. 3.Department of MathematicsWest University of TimişoaraTimişoaraRomania

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