Low-Regularity Solutions of the Periodic Camassa–Holm Equation

2007/01/04 by Camillo De Lellis, Thomas Kappeler, Peter Topalov · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic structures and combinatorial models #Boundary (topology) #Camassa–Holm equation #Connection (principal bundle) #Diffeomorphism #Geodesic #Integrable system #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pointwise #Pure mathematics #Subsequence #Uniqueness

paper · doi:10.1080/03605300601091470

openalex publication_date 2007/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We prove local existence and uniqueness of weak solutions of the Camassa–Holm equation with periodic boundary conditions in various spaces of low-regularity which include the periodic peakons. The proof uses the connection of the Camassa–Holm equation with the geodesic flow on the diffeomorphism group of the circle with respect to the L 2 metric.

Citations

• Tools for PDE
• A New Integrable Shallow Water Equation
• A note on well-posedness for Camassa–Holm equation
• Classical solutions of the periodic Camassa—Holm equation
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Global Conservative Solutions of the Camassa–Holm Equation
• Global Weak Solutions for a Shallow Water Equation
• On the Cauchy problem for the Camassa–Holm equation
• The inverse function theorem of Nash and Moser
• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Euler equations on homogeneous spaces and Virasoro orbits
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Wave breaking for nonlinear nonlocal shallow water equations
• Geodesic flow on the diffeomorphism group of the circle
• A Nonlinear Analysis of the Averaged Euler Equations
• Multipeakons and the Classical Moment Problem

Cited by

• Camassa–Holm equation [wikipedia]