Embedding Camassa-Holm equations in incompressible Euler
Analysis of PDEs
2018-05-01 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.1804.11080,
title = {Embedding Camassa-Holm equations in incompressible Euler},
author = {François-Xavier Vialard and Andrea Natale},
journal= {arXiv preprint arXiv:1804.11080},
year = {2018}
}