The metric completion of Diff([0,1]) with the H^1 right-invariant metric is the space of increasing maps of [0,1] fixing the endpoints.
Embedding Camassa-Holm equations in incompressible Euler
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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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math.OC 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Metric completion of $Diff([0,1])$ with the $H1$ right-invariant metric
The metric completion of Diff([0,1]) with the H^1 right-invariant metric is the space of increasing maps of [0,1] fixing the endpoints.