GENERIC REGULARITY OF CONSERVATIVE SOLUTIONS TO CAMASSA-HOLM TYPE EQUATIONS

被引：10
|
作者：
Li, Mingjie [1 ]
Zhang, Qingtian [2 ]
机构：
[1] Minzu Univ China, Coll Sci, Beijing 100081, Peoples R China
[2] Univ Calif Davis, Dept Math, Davis, CA 95616 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2017年 / 49卷 / 04期
基金：
美国国家科学基金会;
关键词：
Camassa Holm equations; conservative weak solutions; generic regularity; singularities; SHALLOW-WATER EQUATION; WEAK SOLUTIONS; DISSIPATIVE SOLUTIONS; GLOBAL EXISTENCE; SYSTEM; UNIQUENESS; LAWS;
D O I：
10.1137/16M1063009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper mainly proves the generic properties of the Camassa Holm equation and the two-component Camassa Holm equation in a sense of Baire category. We reveal their differences in generic regularity and singular behavior.
引用
收藏
页码：2920 / 2949
页数：30
相关论文
共 50 条
  • [41] Solutions of the Camassa-Holm Equation Near the Soliton
    Ding, Dan-ping
    Lu, Wei
    ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2023, 39 (02): : 450 - 464
  • [42] Global solutions for the modified Camassa-Holm equation
    Ji, Shuguan
    Zhou, Yonghui
    ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2022, 102 (10):
  • [43] A note on the Camassa-Holm equation
    Coclite, G. M.
    Karlsen, K. H.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (06) : 2158 - 2166
  • [44] Periodic Conservative Solutions for a Modified Two-Component Camassa-Holm System with Peakons
    Wang, Yujuan
    Song, Yongduan
    ABSTRACT AND APPLIED ANALYSIS, 2013,
  • [45] The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation
    Li, Nan
    Lai, Shaoyong
    Li, Shuang
    Wu, Meng
    ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [46] Global conservative solution for a dissipative Camassa-Holm type equation with cubic and quartic nonlinearities
    Deng, Wenjie
    Yin, Zhaoyang
    APPLICABLE ANALYSIS, 2023, 102 (08) : 2365 - 2379
  • [47] Well-posedness of modified Camassa-Holm equations
    McLachlan, Robert
    Zhang, Xingyou
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (08) : 3241 - 3259
  • [48] Lipschitz metric for conservative solutions of the two-component Camassa-Holm system
    Cai, Hong
    Chen, Geng
    Shen, Yannan
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2017, 68 (01):
  • [49] Lyapunov-type stability criterion for periodic generalized Camassa-Holm equations
    Jiang, Ke
    Cao, Feng
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 74
  • [50] The Cauchy problem for a family of generalized Camassa-Holm equations
    Tu, Xi
    Yin, Zhaoyang
    APPLICABLE ANALYSIS, 2016, 95 (06) : 1184 - 1213
12345