The Cauchy problem for the generalized Camassa-Holm equation in Besov space

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	The Cauchy problem for the generalized Camassa-Holm equation in Besov space
	Yan, Wei 1; Li, Yongsheng 2; Zhang, Yimin 3
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2014-04-15
卷号	256 期号:8 页码:2876-2901
关键词	Cauchy problem Generalized Camassa-Holm equation Besov spaces Osgood Lemma Blow-up criterion
英文摘要	In this paper we consider the Cauchy problem for the generalized Camassa-Holm equation u(t) + u(Q)u(x) + partial derivative(x)(1 - partial derivative(2)(x))(-1) [2ku + Q(2)+3Q/2(Q+1)u(Q+1) + Q/2u(Q-1)u(x)(2)] = 0 in Besov space. First, we prove that the solutions to the Cauchy problem for the generalized Camassa-Holm equation do not depend uniformly continuously on the initial data in H-s(R) with s < 3/2 when k = 0. Second, combining the real interpolations among inhomogeneous Besov spaces with Lemma 5.2.1 of [6] which is called Osgood Lemma (a substitute for Gronwall inequality), we show that the Cauchy problem for the generalized Camassa-Holm equation is locally well-posed in B-2,1(3/2). Finally, we give a blow-up criterion. (C) 2014 Elsevier Inc. All rights reserved.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Mathematics
研究领域[WOS]	Mathematics
关键词[WOS]	SHALLOW-WATER EQUATION ; GLOBAL WEAK SOLUTIONS ; WELL-POSEDNESS ; CH EQUATION ; NONUNIFORM DEPENDENCE ; WAVE SOLUTIONS ; STABILITY ; BREAKING ; PEAKONS ; EXISTENCE
收录类别	SCI
语种	英语
WOS记录号	WOS:000331849000010
公开日期	2015-07-14
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/1286]
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 in Besov space[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2014,256(8):2876-2901.
APA	Yan, Wei,Li, Yongsheng,&Zhang, Yimin.(2014).The Cauchy problem for the generalized Camassa-Holm equation in Besov space.JOURNAL OF DIFFERENTIAL EQUATIONS,256(8),2876-2901.
MLA	Yan, Wei,et al."The Cauchy problem for the generalized Camassa-Holm equation in Besov space".JOURNAL OF DIFFERENTIAL EQUATIONS 256.8(2014):2876-2901.