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] Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space
Tu, Xi
Yin, Zhaoyang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 128 : 1 - 19
[3] 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
[4] Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space
Tu, Xi
Yin, Zhaoyang
MONATSHEFTE FUR MATHEMATIK, 2020, 191 (04): : 801 - 829
[5] Well-posedness of modified Camassa-Holm equations
McLachlan, Robert
Zhang, Xingyou
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (08) : 3241 - 3259
[6] LOCAL WELL-POSEDNESS AND BLOW-UP PHENOMENA FOR A GENERALIZED CAMASSA-HOLM EQUATION WITH PEAKON SOLUTIONS
Tu, Xi
Yin, Zhaoyang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (05) : 2781 - 2801
[7] Sharp ill-posedness for the generalized Camassa-Holm equation in Besov spaces
Li, Jinlu
Yu, Yanghai
Zhu, Weipeng
JOURNAL OF EVOLUTION EQUATIONS, 2022, 22 (01)
[8] 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):
[9] WELL-POSEDNESS AND BLOW-UP PHENOMENA FOR A GENERALIZED CAMASSA-HOLM EQUATION
Li, Jinlu
Yin, Zhaoyang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (10) : 5493 - 5508
[10] 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

← 1 2 3 4 5 →