LOCAL WELL-POSEDNESS AND BLOW-UP PHENOMENA FOR A GENERALIZED CAMASSA-HOLM EQUATION WITH PEAKON SOLUTIONS

被引：2

作者：

Tu, Xi ^{[1
]}

Yin, Zhaoyang ^{[1
,2
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 05期

关键词：

A generalized Camassa-Holm equation; local well-posedness; Besov spaces; blow-up; peakon solutions; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; CAUCHY-PROBLEM; INTEGRABLE EQUATION; WAVE SOLUTIONS; SHOCK-WAVES; EXISTENCE; TRAJECTORIES; BREAKING;

D O I：

10.3934/dcds.2016.36.2781

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion. Finally, we verify that the system possesses peakon solutions.

引用

页码：2781 / 2801

页数：21

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