Ill-posedness for the Camassa-Holm and related equations in Besov spaces

被引：29

作者：

Li, Jinlu ^{[1
]}

Yu, Yanghai ^{[2
]}

Zhu, Weipeng ^{[3
]}

机构：

[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China

[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

[3] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 306卷

基金：

中国国家自然科学基金;

关键词：

Camassa-Holm equation; Shallow water wave models; Ill-posedness; Besov space; SHALLOW-WATER EQUATION; WELL-POSEDNESS; NONUNIFORM DEPENDENCE; CAUCHY-PROBLEM; INITIAL DATA; EXISTENCE; TRAJECTORIES; STABILITY; BREAKING; FAMILY;

D O I：

10.1016/j.jde.2021.10.052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a construction of u(0) is an element of B-p,infinity(sigma) such that the corresponding solution to the Camassa-Holm equation starting from u(0) is discontinuous at t = 0 in the metric of B-p,infinity(sigma), which implies the ill-posedness for this equation in B-p,infinity(sigma). We also apply our method to the b-equation and Novikov equation. (C) 2021 Published by Elsevier Inc.

引用

页码：403 / 417

页数：15

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