Blow-up, global existence and persistence properties for the coupled Camassa-Holm equations

DOI10.1007/s11040-011-9094-2zbMath1245.35115OpenAlexW2032297425MaRDI QIDQ430049

Mingxuan Zhu

Publication date: 20 June 2012

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11040-011-9094-2

zbMATH Keywords

global existenceblow-up ratepersistence propertiescoupled Camassa-Holm equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44)

Related Items (11)

Some properties of the solutions of the \(N\)-component Camassa-Holm system with peakons ⋮ Initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval ⋮ The Cauchy problem for a weakly dissipative 2-component Camassa-Holm system ⋮ The Cauchy problem for a two-component Novikov equation in the critical Besov space ⋮ Persistence properties of solutions to the dissipative 2-component Degasperis-Procesi system ⋮ On an \(N\)-component Camassa-Holm equation with peakons ⋮ Blowup phenomena for a modified Dullin-Gottwald-Holm shallow water system ⋮ On a three-component Camassa-Holm equation with peakons ⋮ Local well-posedness in the critical Besov space and blow-up for an \(n\)-component Camassa-Holm system ⋮ Non‐uniform dependence and persistence properties for coupled Camassa–Holm equations ⋮ The local well-posedness and global solution for a modified periodic two-component Camassa-Holm system

Cites Work

• Analyticity of periodic traveling free surface water waves with vorticity
• On a two-component Degasperis-Procesi shallow water system
• The trajectories of particles in Stokes waves
• Blow-up of solutions to a periodic nonlinear dispersive rod equation
• The Cauchy problem for a two-component generalized \(\theta \)-equations
• Well-posedness and blow-up solution for a modified two-component periodic Camassa-Holm system with peakons
• Blow-up of solutions to the DGH equation
• Persistence properties for a family of nonlinear partial differential equations
• Wave breaking for nonlinear nonlocal shallow water equations
• On the Cauchy problem for the periodic Camassa-Holm equation
• Stokes waves
• Special issue on the occasion of the 50th volume
• Breakdown of a shallow water equation
• Wave breaking for a shallow water equation
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Persistence properties and unique continuation of solutions of the Camassa-Holm equation
• Blow-up and global solutions to a new integrable model with two components
• Finite propagation speed for the Camassa–Holm equation
• A new asymptotic behavior of solutions to the Camassa-Holm equation
• On Solutions to a Two-Component Generalized Camassa-Holm Equation
• Well posedness and blow-up solution for a new coupled Camassa–Holm equations with peakons
• Particle trajectories in solitary water waves
• Compactly Supported Solutions of the Camassa-Holm Equation
• Blow-up phenomenon for a periodic rod equation

This page was built for publication: Blow-up, global existence and persistence properties for the coupled Camassa-Holm equations