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.
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页码：403 / 417
页数：15
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