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## Section: New Results

### Embedding Camassa-Holm equations in incompressible Euler

A. Natale, F-X. Vialard. In [13] : In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the $H\left(\mathrm{div}\right)$ 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.