The Cauchy problem for the generalized Camassa-Holm equation

被引：2
|
作者：
Yan, Wei [1 ]
Li, Yongsheng [2 ]
Zhang, Yimin [3 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
[2] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
[3] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China
来源：
APPLICABLE ANALYSIS | 2014年 / 93卷 / 07期
关键词：
Cauchy problem; generalized Camassa-Holm equation; Besov spaces; ill-posedness; 35G25; 35L05; 35R25; SHALLOW-WATER EQUATION; WELL-POSEDNESS; WAVE SOLUTIONS; STABILITY; BREAKING; EXISTENCE;
D O I：
10.1080/00036811.2013.833325
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation. By using the littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the generalized Camassa-Holm equation is locally well posed in the Besov space B-p,r(s) with 1 <= p, r <= + infinity and s > max {1+1/p, 3/3} which generalizes the local well-posedness result in [1]. We also establish the ill-posedness result of the generalized Camassa-Holm equation and give a blow-up criterion.
引用
收藏
页码：1358 / 1381
页数：24
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