The Cauchy problem for a weakly dissipative 2-component Camassa-Holm system
type: Item
instance of: scholarly article
title: The Cauchy problem for a weakly dissipative 2-component Camassa-Holm system
zbMATH Open document ID: 1407.35178
DOI: 10.1155/2014/801941
author: Sen Ming
author: Han Yang
author: Yonghong Wu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The weakly dissipative 2-component Camassa-Holm system is considered. A local well-posedness for the system in Besov spaces is established by using the Littlewood-Paley theory and a priori estimates for the solutions of transport equation. The wave-breaking mechanisms and the exact blow-up rate of strong solutions to the system are presented. Moreover, a global existence result for strong solutions is derived.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35D35
zbMATH DE Number: 7017293
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/801941
OpenAlex ID: W1991033976
Wikidata QID: Q59069338
cites work: An integrable shallow water equation with peaked solitons
cites work: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
cites work: The trajectories of particles in Stokes waves
cites work: Particle trajectories in solitary water waves
cites work: Stability of peakons
cites work: Stability of the Camassa-Holm solitons
cites work: Stability of a class of solitary waves in compressible elastic rods
cites work: Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
cites work: 一类弱耗散Camassa-Holm方程局部强解的适定性及弱解的存在性
cites work: The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation
cites work: Global solutions and blow-up phenomena to a shallow water equation
cites work: A model containing both the Camassa-Holm and Degasperis-Procesi equations
cites work: The study of global weak solutions for a generalized hyperelastic-rod wave equation
cites work: Well-posedness and blow-up phenomena for a higher order shallow water equation
cites work: Global existence for the higher-order Camassa-Holm shallow water equation
cites work: Global structure instability of Riemann solutions of quasilinear hyperbolic systems of conservation laws: rarefaction waves
cites work: On existence and uniqueness of the global weak solution for a shallow water equation
cites work: Well-posedness and analyticity for the Cauchy problem for the generalized Camassa-Holm equation
cites work: Global existence and blow-up phenomena for the weakly dissipative Camassa-Holm equation
cites work: On an integrable two-component Camassa-Holm shallow water system
cites work: On the Cauchy problem for a two-component Degasperis-Procesi system
cites work: Analytic solutions of the Cauchy problem for two-component shallow water systems
cites work: Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system
cites work: Global weak solutions for a two-component Camassa-Holm shallow water system
cites work: Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
cites work: On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
cites work: On the Cauchy problem for the two-component Camassa-Holm system
cites work: A two-component generalization of the Camassa-Holm equation and its solutions
cites work: Blow-up, global existence and persistence properties for the coupled Camassa-Holm equations
cites work: Persistence properties and unique continuation of solutions to a two-component Camassa-Holm equation
cites work: Unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations
cites work: Wave breaking of an integrable Camassa-Holm system with two components
cites work: Q4657352
cites work: On the local well posedness and blow-up solution of a coupled Camassa-Holm equations in Besov Spaces
cites work: Blow up and Blow-up rate for the generalized 2-component Camassa-Holm equation
cites work: Wave breaking for a generalized weakly dissipative two-component Camassa-Holm system
cites work: Well-posedness, wave breaking and peakons for a modified \({\mu}\)-Camassa-Holm equation
cites work: On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity
cites work: A few remarks on the Camassa-Holm equation.
cites work: On the uniqueness in critical spaces for compressible Navier-Stokes equations
cites work: The Cauchy problem for the integrable Novikov equation
cites work: Fourier Analysis and Nonlinear Partial Differential Equations
cites work: On the Cauchy problem for an integrable equation with peakon solutions
cites work: Wave breaking for nonlinear nonlocal shallow water equations
cites work: Special issue on the occasion of the 50th volume
description: scientific article; zbMATH DE number 7017293