Non-uniform dependence and persistence properties for coupled Camassa-Holm equations

被引：5

作者：

Zhou, Shouming ^{[1
]}

机构：

[1] Chongqing Normal Univ, Coll Math Sci, Chongqing 41331, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 10期

关键词：

non-uniform dependence; persistence properties; coupled Camassa-Holm equations; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; WELL-POSEDNESS; WAVE-BREAKING; 2-COMPONENT; EXISTENCE; SCATTERING; STABILITY;

D O I：

10.1002/mma.4258

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the non-uniform dependence and persistence properties for a coupled Camassa-Holm equations. Using the method of approximate solutions in conjunction with well-posedness estimate, it is proved that the solution map of the Cauchy problem for this coupled Camassa-Holm equation is not uniformly continuous in Sobolev spaces H-s with s>3/2. On the other hand, the persistence properties in weighted L-p spaces for the solution of this coupled Camassa-Holm system are considered. Copyright (c) 2016 John Wiley & Sons, Ltd.

引用

页码：3718 / 3732

页数：15

共 50 条

[21] Non-Uniform Dependence on Initial Data for the Rotation-Camassa-Holm Equation [J].

Xiao, Li ;

Qi, Xueyuan ;

Li, Fengquan .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2022, 24 (04)

[22] Attractor for a Viscous Coupled Camassa-Holm Equation [J].

Tian, Lixin ;

Xu, Ying .

ADVANCES IN DIFFERENCE EQUATIONS, 2010,

[23] Non-uniform dependence and well-posedness for the rotation-Camassa-Holm equation on the torus [J].

Zhang, Lei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (09) :5049-5083

[24] Non-uniform Continuity of the Generalized Camassa-Holm Equation in Besov Spaces [J].

Li, Jinlu ;

Wu, Xing ;

Zhu, Weipeng ;

Guo, Jiayu .

JOURNAL OF NONLINEAR SCIENCE, 2023, 33 (01)

[25] Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit [J].

Li, Jinlu ;

Yu, Yanghai ;

Zhu, Weipeng .

MONATSHEFTE FUR MATHEMATIK, 2024, 205 (01) :177-185

[26] Equations of the Camassa-Holm hierarchy [J].

Ivanov, R. I. .

THEORETICAL AND MATHEMATICAL PHYSICS, 2009, 160 (01) :952-959

[27] The properties of solutions to the dissipative 2-component Camassa-Holm system [J].

Ming, Sen ;

Yang, Han ;

Chen, Zili ;

Yong, Ls .

APPLICABLE ANALYSIS, 2016, 95 (06) :1165-1183

[28] Wave-breaking and persistence properties in weighted LP spaces for a Camassa-Holm type equation with quadratic and cubic nonlinearities [J].

Cheng, Wenguang ;

Lin, Ji .

MONATSHEFTE FUR MATHEMATIK, 2024, 205 (01) :103-117

[29] Local well-posedness and persistence properties for a model containing both Camassa-Holm and Novikov equation [J].

Zhou, Shouming ;

Wu, Chun ;

Zhang, Baoshuai .

BOUNDARY VALUE PROBLEMS, 2014,

[30] The Cauchy problem for coupled system of the generalized Camassa-Holm equations [J].

Ming, Sen ;

Du, Jiayi ;

Ma, Yaxian .

AIMS MATHEMATICS, 2022, 7 (08) :14738-14755

← 1 2 3 4 5 →