Blow-up phenomena and the local well-posedness and ill-posedness of the generalized Camassa-Holm equation in critical Besov spaces

被引：1

作者：

Meng, Zhiying ^{[1
]}

Yin, Zhaoyang ^{[1
,2
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China

[2] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2023年 / 200卷 / 04期

关键词：

A generalized Camassa-Holm equation; Local well-posedness; Blow-up; Ill-posedness; GLOBAL CONSERVATIVE SOLUTIONS; SHALLOW-WATER EQUATION; CAUCHY-PROBLEM; WEAK SOLUTIONS; EXISTENCE;

D O I：

10.1007/s00605-022-01719-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first establish the local well-posednesss for the Cauchy problem of a generalized Camassa-Holm (gCH) equation in Besov spaces B-p,1(1+1p) with 1 <= p<+infinity Then we gain two blow-up criterions, and present two new blow-up results. Finally, we prove the ill-posedness of the gCH equation in critical Besov spaces B-2,r(3/2),r is an element of(1,+infinity].

引用

页码：933 / 954

页数：22

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