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Embedding Camassa-Holm equations in incompressible Euler

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CH computational_v1.pdf (384.6Kb)
Date
2019
Dewey
Analyse
Sujet
Eisenhart lift; Incompressible Euler equation; Camassa-Holm equation; Dimension theory, Poincaré recurrences, multifractal analysis
Journal issue
Journal of Geometric Mechanics
Volume
11
Number
2
Publication date
2019
Article pages
205-223
DOI
http://dx.doi.org/10.3934/jgm.2019011
URI
https://basepub.dauphine.fr/handle/123456789/17943
Collections
  • CEREMADE : Publications
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Author
Natale, Andrea
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vialard, François-Xavier
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the incompressible Euler equation of a non compact Riemannian manifold. The method consists in embedding the incompressible Euler equation with a potential term coming from classical mechanics into incompressible Euler of a manifold and seeing the CH2 equation as a particular case of such fluid dynamic equation.

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