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
相关论文
共 50 条
  • [21] Well-posedness and peakons for a higher-order μ-Camassa-Holm equation
    Wang, Feng
    Li, Fengquan
    Qiao, Zhijun
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 175 : 210 - 236
  • [22] Energy conservation and well-posedness of the Camassa-Holm equation in Sobolev spaces
    Guo, Yingying
    Ye, Weikui
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2023, 74 (05):
  • [23] Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces
    Li, Jinlu
    Yin, Zhaoyang
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (11) : 6125 - 6143
  • [24] WELL-POSEDNESS FOR A MODIFIED TWO-COMPONENT CAMASSA-HOLM SYSTEM IN CRITICAL SPACES
    Yan, Kai
    Yin, Zhaoyang
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (04) : 1699 - 1712
  • [25] Wave-breaking and persistence properties in weighted LP spaces for a Camassa-Holm type equation with quadratic and cubic nonlinearities
    Cheng, Wenguang
    Lin, Ji
    MONATSHEFTE FUR MATHEMATIK, 2024, 205 (01): : 103 - 117
  • [26] Well-posedness and Large Deviations of the Stochastic Modified Camassa-Holm Equation
    Chen, Yong
    Gao, Hongjun
    POTENTIAL ANALYSIS, 2016, 45 (02) : 331 - 354
  • [27] New wave breaking for the Camassa-Holm equation
    Han, Runjie
    Yang, Shaojie
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 422 : 604 - 613
  • [28] LOCAL WELL-POSEDNESS AND BLOW-UP PHENOMENA FOR A GENERALIZED CAMASSA-HOLM EQUATION WITH PEAKON SOLUTIONS
    Tu, Xi
    Yin, Zhaoyang
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (05) : 2781 - 2801
  • [29] Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities
    Miao, Yingting
    Rohde, Christian
    Tang, Hao
    STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2024, 12 (01): : 614 - 674
  • [30] On the Wave-Breaking Phenomena and Global Existence for the Generalized Periodic Camassa-Holm Equation
    Gui, Guilong
    Liu, Yue
    Zhu, Min
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012, 2012 (21) : 4858 - 4903
12345