On the Cauchy problem of a three-component Camassa--Holm equations

Xinglong  Wu

doi:10.3934/dcds.2016.36.2827

Article Contents

2016, Volume 36, Issue 5: 2827-2854. Doi: 10.3934/dcds.2016.36.2827

This issue Previous Article Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems Next Article A note on quasilinear wave equations in two space dimensions

On the Cauchy problem of a three-component Camassa--Holm equations

Xinglong Wu^1,

1.
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071

Received: March 2015

Revised: April 2015

Published: May 2017

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Abstract

The present paper is mainly concerned with the well-posedness, blow-up phenomena and exponential decay of solution. The well-posedness for a three-component Camassa--Holm equation is established in a critical Besov space. Comparing with the result of Hu, ect. in the paper [25], a new wave-breaking solution is obtained. The exponential decay of solution in our paper covers and extents the corresponding results in [12,24,31].

Keywords:

A three-component Camassa--Holm equations,
a critical Besov space,
blow-up phenomena,
the exponential decay,
wave-breaking,
traveling wave solutions.

Mathematics Subject Classification: 35G25, 35L05.

Citation:

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