Non-uniform Continuity of the Generalized Camassa-Holm Equation in Besov Spaces

被引：3
|
作者：
Li, Jinlu [1 ]
Wu, Xing [2 ]
Zhu, Weipeng [3 ]
Guo, Jiayu [1 ]
机构：
[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Jiangxi, Peoples R China
[2] Henan Agr Univ, Coll Informat & Management Sci, Zhengzhou 450002, Henan, Peoples R China
[3] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
来源：
JOURNAL OF NONLINEAR SCIENCE | 2023年 / 33卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Generalized Camassa-Holm equation; Non-uniform continuous dependence; Besov spaces; WELL-POSEDNESS; CAUCHY-PROBLEM; ILL-POSEDNESS; INITIAL DATA; DEPENDENCE; ANALYTICITY;
D O I：
10.1007/s00332-022-09866-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation proposed by Hakkaev and Kirchev (Commun Partial Differ Equ 30:761-781, 2005). We prove that the solution map of the generalized Camassa-Holm equation is not uniformly continuous on the initial data in Besov spaces. Our result includes the present work Li et al. (Differ Equ 269:8686-8700, 2020) on Camassa-Holm equation with Q = 1 and extends the previous non-uniform continuity in Sobolev spaces Mi and Mu (Monatsh Math 176:423-457, 2015) to Besov spaces.
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页数：11
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