The Cauchy problem for the generalized Camassa-Holm equation

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	The Cauchy problem for the generalized Camassa-Holm equation
	Yan, Wei 1; Li, Yongsheng 2; Zhang, Yimin 3
刊名	APPLICABLE ANALYSIS
	2014-07-03
卷号	93 期号:7 页码:1358-1381
关键词	Cauchy problem generalized Camassa-Holm equation Besov spaces ill-posedness 35G25 35L05 35R25
英文摘要	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.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Mathematics, Applied
研究领域[WOS]	Mathematics
关键词[WOS]	SHALLOW-WATER EQUATION ; WELL-POSEDNESS ; WEAK SOLUTIONS ; WAVE SOLUTIONS ; BESOV-SPACES ; STABILITY ; BREAKING ; PEAKONS ; EXISTENCE ; SOLITONS
收录类别	SCI
语种	英语
WOS记录号	WOS:000335945700002
公开日期	2015-07-14
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/1491]
专题	武汉物理与数学研究所_数学物理与应用研究部
作者单位	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
推荐引用方式 GB/T 7714	Yan, Wei,Li, Yongsheng,Zhang, Yimin. The Cauchy problem for the generalized Camassa-Holm equation[J]. APPLICABLE ANALYSIS,2014,93(7):1358-1381.
APA	Yan, Wei,Li, Yongsheng,&Zhang, Yimin.(2014).The Cauchy problem for the generalized Camassa-Holm equation.APPLICABLE ANALYSIS,93(7),1358-1381.
MLA	Yan, Wei,et al."The Cauchy problem for the generalized Camassa-Holm equation".APPLICABLE ANALYSIS 93.7(2014):1358-1381.