Riemannian geometry on the diffeomorphism group of the circle

DOI10.1007/s11512-007-0047-8zbMath1149.58003OpenAlexW2060901140WikidataQ115377883 ScholiaQ115377883MaRDI QIDQ942030

Jonatan Lenells

Publication date: 3 September 2008

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11512-007-0047-8

zbMATH Keywords

Euler equationCamassa-Holm equationgroup of diffeomorphismsBanach manifoldsinfinite-dimensional manifolds

Mathematics Subject Classification ID

Related Items (9)

On the smoothness of the geodesic spray for the Camassa-Holm equation ⋮ On a two-component \(\pi \)-Camassa-Holm system ⋮ Geometric approach on the global conservative solutions of the Camassa-Holm equation ⋮ The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations ⋮ Stability of periodic peakons for a nonlinear quartic \(\mu\)-Camassa-Holm equation ⋮ Curvature computations for a two-component Camassa-Holm equation with vorticity ⋮ The two‐component Camassa‐Holm system in weighted L_p spaces ⋮ Global existence and blow-up for a weakly dissipative \(\mu\)DP equation ⋮ Non-metric two-component Euler equations on the circle

Cites Work

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• Integrability of invariant metrics on the diffeomorphism group of the circle
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• Groups of diffeomorphisms and the motion of an incompressible fluid
• Traveling wave solutions of the Camassa-Holm equation
• The inverse function theorem of Nash and Moser
• Dynamics of Director Fields
• A shallow water equation on the circle
• Breakdown of the Camassa-Holm equation
• On the geometric approach to the motion of inertial mechanical systems
• An integrable shallow water equation with peaked solitons
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group

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