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.

引用

页数：11

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