Kahler geometry and Burgers' vortices

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TitreKahler geometry and Burgers' vortices
Type de publicationCommunication
TypeCommunication avec actes dans un congrès
Date du colloque27-29/08/2009
Titre du colloqueUkrainian Mathematical Congress
Titre des actes ou de la revueProceedings of Institute of Mathematics of National Academy of Sciences of Ukraine
Pagination303 - 321
AuteurRoulstone, Ian, Banos, Bertrand, Gibbon, J. D, Roubtsov, Vladimir
EditeurInstitute of Mathematics of National Academy of Sciences of Ukraine
Résumé en anglais

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-Amp`ere 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-Amp`ere equation. We then show how this structure can be extended to a class of canonical vortex structures in three dimensions.

URL de la noticehttp://okina.univ-angers.fr/publications/ua65
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