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Embedding Camassa-Holm equations in incompressible Euler

Natale, Andrea; Vialard, François-Xavier (2019), Embedding Camassa-Holm equations in incompressible Euler, Journal of Geometric Mechanics, 11, 2, p. 205-223. 10.3934/jgm.2019011

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Journal of Geometric Mechanics
Volume
11
Number
2
Pages
205-223
Publication identifier
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Author(s)
Natale, Andrea
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vialard, François-Xavier
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
Eisenhart lift; Incompressible Euler equation; Camassa-Holm equation; Dimension theory, Poincaré recurrences, multifractal analysis