Ill-posedness for the Camassa-Holm and related equations in Besov spaces

被引：29
|
作者：
Li, Jinlu [1 ]
Yu, Yanghai [2 ]
Zhu, Weipeng [3 ]
机构：
[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China
[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China
[3] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 306卷
基金：
中国国家自然科学基金;
关键词：
Camassa-Holm equation; Shallow water wave models; Ill-posedness; Besov space; SHALLOW-WATER EQUATION; WELL-POSEDNESS; NONUNIFORM DEPENDENCE; CAUCHY-PROBLEM; INITIAL DATA; EXISTENCE; TRAJECTORIES; STABILITY; BREAKING; FAMILY;
D O I：
10.1016/j.jde.2021.10.052
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we give a construction of u(0) is an element of B-p,infinity(sigma) such that the corresponding solution to the Camassa-Holm equation starting from u(0) is discontinuous at t = 0 in the metric of B-p,infinity(sigma), which implies the ill-posedness for this equation in B-p,infinity(sigma). We also apply our method to the b-equation and Novikov equation. (C) 2021 Published by Elsevier Inc.
引用
收藏
页码：403 / 417
页数：15
相关论文
共 50 条
  • [1] Sharp ill-posedness for the generalized Camassa-Holm equation in Besov spaces
    Li, Jinlu
    Yu, Yanghai
    Zhu, Weipeng
    JOURNAL OF EVOLUTION EQUATIONS, 2022, 22 (01)
  • [2] Ill-posedness of the Camassa-Holm and related equations in the critical space
    Guo, Zihua
    Liu, Xingxing
    Molinet, Luc
    Yin, Zhaoyang
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (2-3) : 1698 - 1707
  • [3] Sharp ill-posedness for the generalized Camassa–Holm equation in Besov spaces
    Jinlu Li
    Yanghai Yu
    Weipeng Zhu
    Journal of Evolution Equations, 2022, 22
  • [4] 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
  • [5] Blow-up phenomena and the local well-posedness and ill-posedness of the generalized Camassa-Holm equation in critical Besov spaces
    Meng, Zhiying
    Yin, Zhaoyang
    MONATSHEFTE FUR MATHEMATIK, 2023, 200 (04): : 933 - 954
  • [6] Ill-posedness for a generalized Camassa-Holm equation with higher-order nonlinearity in the critical Besov space
    Deng, Wei
    Li, Min
    Wu, Xing
    Zhu, Weipeng
    MONATSHEFTE FUR MATHEMATIK, 2024, 203 (04): : 843 - 857
  • [7] Ill-posedness for the Euler equations in Besov spaces
    Li, Jinlu
    Yu, Yanghai
    Zhu, Weipeng
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 74
  • [8] Well-posedness of the modified Camassa-Holm equation in Besov spaces
    Tang, Hao
    Liu, Zhengrong
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (04): : 1559 - 1580
  • [9] Spiked traveling waves and ill-posedness for the Camassa-Holm equation on the circle
    Byers, P
    ILLINOIS JOURNAL OF MATHEMATICS, 2004, 48 (03) : 1031 - 1040
  • [10] Ill-posedness for the Cauchy problem of the Camassa-Holm equation in B∞,11 (R)
    Guo, Yingying
    Ye, Weikui
    Yin, Zhaoyang
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 327 : 127 - 144
12345