On the global weak solutions for a modified two-component Camassa-Holm equation

被引：14
作者：
Guan, Chunxia [1 ]
Yin, Zhaoyang [2 ]
机构：
[1] Sun Yat Sen Univ, Inst Francochinois Energie Nucl, Guangzhou 510275, Guangdong, Peoples R China
[2] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
来源：
MATHEMATISCHE NACHRICHTEN | 2013年 / 286卷 / 13期
关键词：
A modified two-component Camassa-Holm equation; global weak solutions; approximation solutions; SHALLOW-WATER EQUATION; BLOW-UP PHENOMENA; WELL-POSEDNESS; CONSERVATIVE SOLUTIONS; DISSIPATIVE SOLUTIONS; BREAKING WAVES; SCATTERING; EXISTENCE; TRAJECTORIES; TRANSFORM;
D O I：
10.1002/mana.201200193
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate the existence of global weak solutions to the Cauchy problem of a modified two-component Camassa-Holm equation with the initial data satisfying lim(x +/-)u(0)(x) = u(+/-). By perturbing the Cauchy problem around a rarefaction wave, we obtain a global weak solution for the system under the assumption u(-) u(+). The global weak solution is obtained as a limit of approximation solutions. The key elements in our analysis are the Helly theorem and the estimation of energy for approximation solutions in H-1(R) x H-1(R) and some a priori estimates on the first-order derivatives of approximation solutions. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
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页码：1287 / 1304
页数：18
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