Well-posedness of the EPDiff equation with a pseudo-differential inertia operator. (English) Zbl 1437.58013
Authors’ abstract: 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.
Reviewer: Nicolai K. Smolentsev (Kemerovo)
MSC:
| 58D05 | Groups of diffeomorphisms and homeomorphisms as manifolds |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
EPDiff equation; diffeomorphism groups; Sobolev metrics of fractional order; Euler-Arnold equation; Frèchet Lie groupReferences:
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