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Kahler geometry and Burgers' vortices

Abstract :

We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two spatial dimensions. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation using Monge-Ampere structures. In two dimensional flows where the laplacian of the pressure is positive, a K¨ahler geometry is described on the phase space of the fluid; in regions where the laplacian of the pressure is negative, a product structure is described. These structures can be related to the ellipticity and hyperbolicity (respectively) of a Monge-Ampere equation. We then show how this structure can be extended to a class of canonical vortex structures in three dimensions.

Type de document :
Communication dans un congrès
Domaine :

https://hal.univ-angers.fr/hal-03031588
Contributeur : Okina Université d'Angers <>
Soumis le : lundi 30 novembre 2020 - 15:20:16
Dernière modification le : jeudi 3 décembre 2020 - 03:25:38
Archivage à long terme le : : lundi 1 mars 2021 - 19:28:12

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roulstone_et_al_2009_kahler_ge...
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Identifiants

• HAL Id : hal-03031588, version 1
• OKINA : ua65

Citation

Ian Roulstone, Bertrand Banos, J. Gibbon, Vladimir Roubtsov. Kahler geometry and Burgers' vortices. Ukrainian Mathematical Congress, Aug 2009, Kiev, Ukraine. pp.303 - 321. ⟨hal-03031588⟩

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