Wave-breaking and weak instability for the stochastic modified two-component Camassa-Holm equations

被引：1
|
作者：
Zhao, Yongye [1 ]
Li, Yongsheng [2 ]
Chen, Fei [3 ]
机构：
[1] Guangzhou Maritime Univ, Dept Basic Courses, Guangzhou 510725, Guangdong, Peoples R China
[2] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China
[3] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2023年 / 74卷 / 04期
关键词：
Stochastic modified two-component Camassa-Holm equations; Wave-breaking; Breaking rate; Stability; Exiting time; SHALLOW-WATER EQUATION; WELL-POSEDNESS; NONUNIFORM DEPENDENCE; INITIAL DATA; BLOW-UP; EXISTENCE; EULER;
D O I：
10.1007/s00033-023-02030-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the stochastic modified two-component Camassa-Holm equations. For the periodic boundary value problem for this SPDE, we first study the local existence, uniqueness and blow-up criterion of a solution in Sobolev spaces H-s with s > 5/2. Particularly, for the linear non-autonomous noise case, we study the wave-breaking phenomenon. When wave-breaking occurs, we estimate the corresponding probability and the breaking rate of the solutions. Finally, we study the noise effect on the dependence on initial data. It is shown that the noise cannot improve the stability of exiting times and the continuity of solution map at the same time.
引用
收藏
页数：27
相关论文
共 50 条
  • [21] A note on a modified two-component Camassa-Holm system
    Jin, Liangbing
    Guo, Zhengguang
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (02) : 887 - 892
  • [22] Weak well-posedness for a modified two-component Camassa-Holm system
    Guan, Chunxia
    Wang, Jianming
    Meng, Yiping
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 178 : 247 - 265
  • [23] BREAKING WAVES FOR THE PERIODIC TWO-COMPONENT CAMASSA-HOLM SYSTEM
    Guo, Fei
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (07) : 2407 - 2415
  • [24] Dependence on initial data for a stochastic modified two-component Camassa-Holm system
    Zhao, Yongye
    Wang, Zhenzhen
    Wu, Yun
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 543 (01)
  • [25] On a two-component π-Camassa-Holm system
    Kohlmann, Martin
    JOURNAL OF GEOMETRY AND PHYSICS, 2012, 62 (04) : 832 - 838
  • [26] On a two-component Camassa-Holm equation
    Zhang, Zixin
    Liu, Q. P.
    APPLIED MATHEMATICS LETTERS, 2025, 165
  • [27] Lipschitz metric for the modified two-component Camassa-Holm system
    Guan, Chunxia
    Yan, Kai
    Wei, Xuemei
    ANALYSIS AND APPLICATIONS, 2018, 16 (02) : 159 - 182
  • [28] Wave breaking for the Stochastic Camassa-Holm equation
    Crisan, Dan
    Holm, Darryl D.
    PHYSICA D-NONLINEAR PHENOMENA, 2018, 376 : 138 - 143
  • [29] Dissipative solutions for the modified two-component Camassa-Holm system
    Wang, Yujuan
    Song, Yongduan
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2014, 21 (03): : 339 - 360
  • [30] Uniqueness of global conservative weak solutions for the modified two-component Camassa-Holm system
    Guan, Chunxia
    JOURNAL OF EVOLUTION EQUATIONS, 2018, 18 (02) : 1003 - 1024
12345