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
收藏
页码：933 / 954
页数：22
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