Local well-posedness of the EPDiff equation: a survey

Abstract

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.

References in corpus (3)

• A New Integrable Equation with Peakon Solutions
• Geometric investigations of a vorticity model equation
• Local and Global Well-posedness of the fractional order EPDiff equation on ${\mathbb{R}}^d$

Cited by in corpus (9)

• Quantum information geometry of driven CFTs
• Vanishing distance phenomena and the geometric approach to SQG
• Semi-invariant Riemannian metrics in hydrodynamics
• Fractional Sobolev metrics on spaces of immersions
• Sobolev metrics on spaces of manifold valued curves
• Can we run to infinity? The diameter of the diffeomorphism group with respect to right-invariant Sobolev metrics
• Fractional Sobolev metrics on spaces of immersed curves
• Regularity and completeness of half-Lie groups
• On Geodesic Completeness for Riemannian Metrics on Smooth Probability Densities