Monge-Ampère Structures and the Geometry of Incompressible Flows

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TitreMonge-Ampère Structures and the Geometry of Incompressible Flows
Type de publicationAutre type de document
AuteurBanos, Bertrand , Roubtsov, Vladimir , Roulstone, Ian
PaysEtats-Unis
Editeur, organisme ou institutionCornell University
VilleIthaca, NY
TypeDocument non publié
Année2015
LangueAnglais
Date28/10/2015
NuméroarXiv:1510.02327
Nombre de pages22
Mots-clésEuler equations Navier-Stokes equations, Monge-Ampère operators
Résumé en anglais

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.

URL de la noticehttp://okina.univ-angers.fr/publications/ua14193