The Cauchy problem for an integrable two-component model with peakon solutions

被引：3

作者：

Mi, Yongsheng ^{[1
,2
]}

Mu, Chunlai ^{[1
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Yangtze Normal Univ, Coll Math & Comp Sci, Fuling 408100, Peoples R China

来源：

APPLICABLE ANALYSIS | 2014年 / 93卷 / 04期

关键词：

Besov spaces; Camassa-Holm-type equation; local well-posedness; 35B30; 35G25; 35A10; 35Q53; SHALLOW-WATER EQUATION; GLOBAL CONSERVATIVE SOLUTIONS; CAMASSA-HOLM EQUATION; GEODESIC-FLOW; DISSIPATIVE SOLUTIONS; BREAKING WAVES; TRAJECTORIES; ANALYTICITY; STABILITY; EXISTENCE;

D O I：

10.1080/00036811.2013.800191

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the Cauchy problem of the new integrable two-componnt system with cubic non-linearity, which was proposed by Xia, Qiao and Zhou. We establish the local well-posedness in a range of the Besov spaces. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time.

引用

页码：840 / 858

页数：19

共 50 条

[31] A note on the Cauchy problem for the two-component Novikov system
Wang, Haiquan
Chong, Gezi
Wu, Lili
JOURNAL OF EVOLUTION EQUATIONS, 2021, 21 (02) : 1809 - 1843
[32] A note on the Cauchy problem for the two-component Novikov system
Haiquan Wang
Gezi Chong
Lili Wu
Journal of Evolution Equations, 2021, 21 : 1809 - 1843
[33] Multi-soliton solutions and the Cauchy problem for a two-component short pulse system
Zhaqilao, Z.
Hu, Qiaoyi
Qiao, Zhijun
NONLINEARITY, 2017, 30 (10) : 3773 - 3798
[34] Bifurcations and Exact Solutions of Generalized Two-Component Peakon Type Dual Systems
Liang, Jianli
Li, Jibin
Zhang, Yi
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2019, 29 (09):
[35] The Cauchy problem and blow-up phenomena of a new integrable two-component Camassa-Holm system
Li, Xiuting
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 132 : 25 - 46
[36] On the Cauchy problem for the modified Novikov equation with peakon solutions
Mi, Yongsheng
Mu, Chunlai
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (03) : 961 - 982
[37] A note on the Cauchy problem for the periodic two-component Novikov system
Wang, Haiquan
Fu, Ying
APPLICABLE ANALYSIS, 2020, 99 (06) : 1042 - 1065
[38] On the Cauchy problem for a two-component Degasperis-Procesi system
Yan, Kai
Yin, Zhaoyang
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) : 2131 - 2159
[39] On the Cauchy problem for the two-component Euler-Poincare equations
Duan, Renjun
Xiang, Zhaoyin
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (08) : 2698 - 2730
[40] On the Cauchy problem of a two-component b-family system
Liu, Jingjing
Yin, Zhaoyang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (06) : 3608 - 3620

← 1 2 3 4 5 →