Local well-posedness of the EPDiff equation: a survey

Boris Kolev (1)

1 I2M - Institut de Mathématiques de Marseille

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 $\mathrm{Diff}(\mathbb{T}^{d})$ and $\mathrm{Diff}(\mathbb{R}^{d})$ when the inertia operator is a non-local Fourier multiplier.

Mots clés: EPDiff equation; diffeomorphism groups; Sobolev metrics of fractional order

Domaines: Physique mathématique [math-ph]

Boris Kolev. Local well-posedness of the EPDiff equation: a survey. Journal of Geometric Mechanics, 2017, Special issue on infinite-dimensional Riemannian geometry, Part I, 9 (2), pp.167-189. ⟨10.3934/jgm.2017007⟩. ⟨hal-01397112⟩