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.
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页数：27
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