The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities

doi:10.1007/s10884-021-10115-0

CSpace

	The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities
	Qin, Guoquan 1,2; Yan, Zhenya 2,3; Guo, Boling 4
	2022-01-16
发表期刊	JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
ISSN	1040-7294
页码	60
摘要	This paper investigates the Cauchy problem of a generalized Camassa-Holm equation with quadratic and cubic nonlinearities (alias the mCH-Novikov-CH equation), which is a generalization of some special equations such as the Camassa-Holm (CH) equation, the modified CH (mCH) equation (alias the Fokas-Olver-Rosenau-Qiao equation), the Novikov equation, the CH-mCH equation, the mCH-Novikov equation, and the CH-Novikov equation. We first show the local well-posedness for the strong solutions of the mCH-Novikov-CH equation in Besov spaces by means of the Littlewood-Paley theory and the transport equations theory. Then, the Holder continuity of the data-to-solution map to this equation are exhibited in some Sobolev spaces. After providing the blow-up criterion and the precise blow-up quantity in light of the Moser-type estimate in the Sobolev spaces, we then trace a portion and the whole of the precise blow-up quantity, respectively, along the characteristics associated with this equation, and obtain two kinds of sufficient conditions on the gradient of the initial data to guarantee the occurance of the wave-breaking phenomenon. Finally, the non-periodic and periodic peakon and multi-peakon solutions for this equation are also explored.
关键词	mCH-Novikov-CH equation Wave breaking Local well-posedness Holder continuity Non-periodic and periodic peakon and multi-peakon solutions
DOI	10.1007/s10884-021-10115-0
收录类别	SCI
语种	英语
资助项目	NSF of China[11925108] ; NSF of China[11731014]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000742792500003
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59869
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Zhenya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
推荐引用方式 GB/T 7714	Qin, Guoquan,Yan, Zhenya,Guo, Boling. The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2022:60.
APA	Qin, Guoquan,Yan, Zhenya,&Guo, Boling.(2022).The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,60.
MLA	Qin, Guoquan,et al."The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities".JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2022):60.