Global existence of weak solutions to the Camassa-Holm equation

2006/01/01 by Erik Wahlén · 32 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Uniqueness #Mathematics #Camassa–Holm equation #Weak solution #Weak formulation #Shallow water equations #Mathematical analysis #Applied mathematics #Integrable system #Boundary value problem

paper · doi:10.1155/imrn/2006/28976

published in International Mathematics Research Notices (Oxford University Press)

openalex publication_date 2006/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We prove the existence and uniqueness of global weak solutions to a shallow water equation. The weak solution setting is important to model the interaction of solitons for this equation.

Citations

• A note on well-posedness for Camassa–Holm equation
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Fredholm determinants and the Camassa‐Holm hierarchy
• ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Global Weak Solutions for a Shallow Water Equation
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• 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
• Orbital stability of solitary waves for a shallow water equation
• Wave breaking for nonlinear nonlocal shallow water equations
• Geodesic flow on the diffeomorphism group of the circle
• On the Cauchy Problem for a Nonlinearly Dispersive Wave Equation

Cited by

• Camassa–Holm equation [wikipedia]