Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces

被引：69

作者：

Li, Jinlu ^{[1
]}

Yin, Zhaoyang ^{[1
,2
]}

机构：

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

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 11期

关键词：

Camassa-Holm type equations; Littlewood-Paley theory; The continuity of the solution map; Nonhomogeneous Besov spaces; BLOW-UP PHENOMENA; GLOBAL WEAK SOLUTIONS; SHALLOW-WATER EQUATION; CAUCHY-PROBLEM; INTEGRABLE EQUATION; WAVE SOLUTIONS; SHOCK-WAVES; EXISTENCE; BREAKING; TRAJECTORIES;

D O I：

10.1016/j.jde.2016.08.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the solution map of the Cauchy problem of Camassa-Holm type equations depends continuously on the initial data in nonhomogeneous Besov spaces in the sense of Hadamard by using the Littlewood-Paley theory and the method introduced by Kato [37] and Danchin [21]. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：6125 / 6143

页数：19

共 50 条

[1] Well-posedness of the modified Camassa-Holm equation in Besov spaces
Tang, Hao
Liu, Zhengrong
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (04): : 1559 - 1580
[2] Well-posedness of modified Camassa-Holm equations
McLachlan, Robert
Zhang, Xingyou
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (08) : 3241 - 3259
[3] Well-posedness of the modified Camassa–Holm equation in Besov spaces
Hao Tang
Zhengrong Liu
Zeitschrift für angewandte Mathematik und Physik, 2015, 66 : 1559 - 1580
[4] Ill-posedness for the Camassa-Holm and related equations in Besov spaces
Li, Jinlu
Yu, Yanghai
Zhu, Weipeng
JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 306 : 403 - 417
[5] Well-posedness of higher-order Camassa-Holm equations
Coclite, G. M.
Holden, H.
Kadsen, K. H.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (03) : 929 - 963
[6] A note on well-posedness for Camassa-Holm equation
Danchin, R
JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 192 (02) : 429 - 444
[7] Well-posedness for stochastic Camassa-Holm equation
Chen, Yong
Gao, Hongjun
Guo, Boling
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (08) : 2353 - 2379
[8] On the well-posedness of the Camassa-Holm equation in the Triebel-Lizorkin spaces
Yang, Minsuk
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 430 (01) : 20 - 31
[9] Energy conservation and well-posedness of the Camassa-Holm equation in Sobolev spaces
Guo, Yingying
Ye, Weikui
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2023, 74 (05):
[10] Local Well-Posedness of a Coupled Camassa-Holm System in Critical Spaces
Liu, Xingxing
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2015, 34 (01): : 43 - 59

← 1 2 3 4 5 →