Well-posedness of the EPDiff equation with a pseudo-differential inertia operator

Abstract : In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-posedness properties for the corresponding Euler-Arnold equations, also called the EPDiff equations, which are of importance in mathematical physics and in the field of shape analysis and template registration. Depending on the order of the metric, we will prove both local and global well-posedness results for these equations. As a result of our analysis we will also obtain new commutator estimates for elliptic pseudo-differential operators.
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Submitted on : Wednesday, November 6, 2019 - 10:30:28 PM
Last modification on : Sunday, November 10, 2019 - 1:24:45 AM

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  • HAL Id : hal-02352635, version 1
  • ARXIV : 1911.03238

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Martin Bauer, Martins Bruveris, Emanuel Cismas, Joachim Escher, Boris Kolev. Well-posedness of the EPDiff equation with a pseudo-differential inertia operator. 2019. ⟨hal-02352635⟩

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