Local well-posedness of the EPDiff equation: A survey

Kolev Boris

doi:10.3934/jgm.2017007

Article Contents

2017, Volume 9, Issue 2: 167-189. Doi: 10.3934/jgm.2017007

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Local well-posedness of the EPDiff equation: A survey

Kolev Boris

Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Received: November 30, 2015

Revised: July 31, 2016

Published: October 2017

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This article is a survey on the local well-posedness problem for the general EPDiff equation. The main contribution concerns recent results on local existence of the geodesics on $\text{Dif}{{\text{f}}^{\infty }}\left( {{\mathbb{T}}^{d}} \right)$ and $\text{Dif}{{\text{f}}^{\infty }}\left( {{\mathbb{R}}^{d}} \right)$ when the inertia operator is a non-local Fourier multiplier.

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Mathematics Subject Classification: Primary: 58D05; Secondary: 35Q35.

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