ON THE CAUCHY PROBLEM FOR A HIGHER-ORDER μ-CAMASSA-HOLM EQUATION

被引：6
|
作者：
Wang, Feng [1 ]
Li, Fengquan [2 ]
Qiao, Zhijun [3 ]
机构：
[1] Xidian Univ, Sch Math & Stat, Xian 710071, Shaanxi, Peoples R China
[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
[3] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 08期
关键词：
Higher-order mu-Camassa-Holm equation; global existence; weak solutions; non-uniformly continuous; peakon solutions; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; DIFFEOMORPHISM GROUP; BLOW-UP; NONUNIFORM DEPENDENCE; WELL-POSEDNESS; STABILITY; BREAKING; METRICS;
D O I：
10.3934/dcds.2018181
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the Cauchy problem of a higher-order mu-Camassa-Holm equation. We first establish the Green's function of (mu - (partial derivative(2)(x)+partial derivative(4)(x))(-1) and local well-posedness for the equation in Sobolev spaces H-s(S), s > 7/2. Then we provide the global existence results for strong solutions and weak solutions. Moreover, we show that the solution map is non-uniformly continuous in H-s(S), s >= 4. Finally, we prove that the equation admits single peakon solutions which have continuous second derivatives and jump discontinuities in the third derivatives.
引用
收藏
页码：4163 / 4187
页数：25
相关论文
共 50 条
  • [1] A NOTE ON THE CAUCHY PROBLEM FOR A HIGHER-ORDER μ-CAMASSA-HOLM EQUATION
    Deng, Xijun
    Chen, Aiyong
    Zhu, Kaixuan
    [J]. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2021, 83 (03): : 107 - 110
  • [2] A note on the cauchy problem for a higher-order µ-camassa-holm equation
    Deng, Xijun
    Chen, Aiyong
    Zhu, Kaixuan
    [J]. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2021, 83 (03): : 107 - 110
  • [3] The Cauchy problem for higher-order modified Camassa-Holm equations on the circle
    Yan, Wei
    Li, Yongsheng
    Zhai, Xiaoping
    Zhang, Yimin
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 187 : 397 - 433
  • [4] On the Cauchy problem for the Camassa-Holm equation
    Rodríguez-Blanco, G
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 46 (03) : 309 - 327
  • [5] On the Cauchy problem of the Camassa-Holm equation
    Dai H.-H.
    Kwek K.-H.
    Gao H.-J.
    Qu C.-C.
    [J]. Frontiers of Mathematics in China, 2006, 1 (1) : 144 - 159
  • [6] A note on the initial value problem for a higher-order Camassa-Holm equation
    Wang, Haiquan
    Guo, Yu
    [J]. MATHEMATISCHE NACHRICHTEN, 2022, 295 (09) : 1783 - 1811
  • [7] The Cauchy problem for a generalized Camassa-Holm equation
    Mi, Yongsheng
    Liu, Yue
    Guo, Boling
    Luo, Ting
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (10) : 6739 - 6770
  • [8] On the Cauchy problem for the generalized Camassa-Holm equation
    Yin, Zhaoyang
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (02) : 460 - 471
  • [9] On the Cauchy problem for the generalized Camassa-Holm equation
    Mi, Yongsheng
    Mu, Chunlai
    [J]. MONATSHEFTE FUR MATHEMATIK, 2015, 176 (03): : 423 - 457
  • [10] On the Cauchy problem for the fractional Camassa-Holm equation
    Mutlubas, N. Duruk
    [J]. MONATSHEFTE FUR MATHEMATIK, 2019, 190 (04): : 755 - 768
12345