A sine-type Camassa-Holm equation: local well-posedness, Holder continuity, and wave-breaking analysis

被引：1
|
作者：
Qin, Guoquan [1 ,2 ]
Yan, Zhenya [2 ,3 ]
Guo, Boling [4 ]
机构：
[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 Mechanizat, 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
来源：
MONATSHEFTE FUR MATHEMATIK | 2022年 / 199卷 / 04期
关键词：
Sine-type Camassa-Holm equation; Well-posedness; Holder continuity; Blow-up criterion and quantity; Wave breaking; SHALLOW-WATER EQUATION; GLOBAL CONSERVATIVE SOLUTIONS; KORTEWEG-DE-VRIES; DISSIPATIVE SOLUTIONS; CAUCHY-PROBLEM; STABILITY; EXISTENCE; PEAKONS; TRAJECTORIES; SCATTERING;
D O I：
10.1007/s00605-022-01670-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we explore the effect of sine-type higher-order nonlinearity on the dispersive dynamics by considering the Cauchy problem for a sine-type Camassa-Holm (alias sine-CH) equation, which is a higher-order generalization of the remarkable CH equation, and also admits the peakon solution. Some main results are presented containing the local well-posedness for strong solutions in subcritical or critical Besov spaces, Holder continuity of the data-to-solution map, the blow-up criterion and the precise blow-up quantity in Sobolev space, and a sufficient condition with regard to the initial data ensuring the occurance of the wave-breaking phenomenon.
引用
收藏
页码：853 / 890
页数：38
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