Local well-posedness and blow-up phenomenon for a generalization two-component Camassa-Holm system

被引：0

作者：

Chen, Yuhui ^{[2
]}

Huang, Jingchi ^{[1
]}

Luo, Wei ^{[1
]}

Yu, Fang ^{[3
]}

机构：

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

[2] Sun Yat Sen Univ, Sch Aeronaut & Astronaut, Guangzhou 510275, Guangdong, Peoples R China

[3] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2019年 / 19卷 / 04期

关键词：

Variational; Two-component Camassa-Holm system; Blow-up; Traveling wave; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; VARIATIONAL DERIVATION; WAVE-BREAKING; EXISTENCE;

D O I：

10.1007/s00028-019-00503-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new generalized two-component Camassa-Holm system is derived via the energy variational approach. This system has two parameters which depend on the energy functional. The initial value problem is investigated. The local well-posedness is obtained when the initial density is away from vacuum. Taking advantage of the method of characteristics and the conservation laws, we prove the blow-up criteria. According to the blow-up criteria, we can prove the finite time blow-up result under some suitable condition. Moreover, we give some exact expression of traveling solutions.

引用

页码：935 / 963

页数：29

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