The Cauchy Problem for the Modified Camassa-Holm Equations

ZHANG Shuanghu; FENG Zhaoyong; YANG Kaibo

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The Cauchy Problem for the Modified Camassa-Holm Equations

更新时间：2023-12-11

- The Cauchy Problem for the Modified Camassa-Holm Equations
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 4, Pages: 8-12(2014)
- 作者机构：
  
  1. ．西南大学数学与统计学院,重庆,400715
  2.  2．中山大学数学与计算科学学院,广东,广州,510275
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 July 2014，
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ZHANG Shuanghu, FENG Zhaoyong, YANG Kaibo. The Cauchy Problem for the Modified Camassa-Holm Equations. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(4):8-12(2014)
DOI：

ZHANG Shuanghu, FENG Zhaoyong, YANG Kaibo. The Cauchy Problem for the Modified Camassa-Holm Equations. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(4):8-12(2014) DOI：

摘要

主要研究修正Camassa-Holm方程的Cauchy问题。首先提出了一个新的爆破结果，这一结果优化了早先获得的一些结果；然后证明了修正 CamassaHolm方程的Cauchy问题在解对初值不一致连续依赖意义下在空间H

(R)

3/2中不适定。

Abstract

The Cauchy problem of the modified Camassa-Holm equation is mainly studied. First

a new blow-up phenomenon which is an improvement of the earlier ones is presented. Then it is proved that the Cauchy problem for the modified Camassa-Holm equation is not locally well-posedness in the sense that its solution does not depend uniformly continuously on the initial data.

关键词

修正 CamassaHolm 方程爆破关于初值非一致依赖性

Keywords

the modified Camassa-Holm equationblow upnon-uniform dependence on initial data

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