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Embedding Camassa-Holm equations in incompressible Euler

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.
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Contributor : François-Xavier Vialard <>
Submitted on : Sunday, April 29, 2018 - 3:40:15 PM
Last modification on : Monday, November 16, 2020 - 2:44:05 PM
Long-term archiving on: : Tuesday, September 25, 2018 - 2:48:38 AM


  • HAL Id : hal-01781162, version 1
  • ARXIV : 1804.11080



Andrea Natale, François-Xavier Vialard. Embedding Camassa-Holm equations in incompressible Euler. Journal of Geometric Mechanics, American Institute of Mathematical Sciences (AIMS), 2019. ⟨hal-01781162⟩



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