# Monge-Ampère Structures and the Geometry of Incompressible Flows

Abstract :

We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to a Monge-Amp\ere structure, and Burgers'-type vortices are a canonical class of solutions associated with this structure. The mapping of such solutions, which are characterised by a linear dependence of the third component of the velocity on the coordinate defining the axis of rotation, to solutions of the incompressible equations in two dimensions is also shown to be an example of a symmetry reduction The Monge-Amp\ere structure for incompressible flow in two dimensions is shown to be hypersymplectic.

Keywords :
Type de document :
Pré-publication, Document de travail
2015

Littérature citée [18 références]

https://hal.archives-ouvertes.fr/hal-01228550
Contributeur : Okina Université d'Angers <>
Soumis le : vendredi 13 novembre 2015 - 13:42:30
Dernière modification le : lundi 5 février 2018 - 15:00:03

### Fichier

1510.02327v2.pdf
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### Identifiants

• HAL Id : hal-01228550, version 2
• OKINA : ua14193

### Citation

Bertrand Banos, Vladimir Roubtsov, Ian Roulstone. Monge-Ampère Structures and the Geometry of Incompressible Flows. 2015. 〈hal-01228550v2〉

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