The Cauchy problem for the generalized Camassa-Holm equation

被引：2

作者：

Yan, Wei ^{[1
]}

Li, Yongsheng ^{[2
]}

Zhang, Yimin ^{[3
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China

[3] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China

来源：

APPLICABLE ANALYSIS | 2014年 / 93卷 / 07期

关键词：

Cauchy problem; generalized Camassa-Holm equation; Besov spaces; ill-posedness; 35G25; 35L05; 35R25; SHALLOW-WATER EQUATION; WELL-POSEDNESS; WAVE SOLUTIONS; STABILITY; BREAKING; EXISTENCE;

D O I：

10.1080/00036811.2013.833325

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation. By using the littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the generalized Camassa-Holm equation is locally well posed in the Besov space B-p,r(s) with 1 <= p, r <= + infinity and s > max {1+1/p, 3/3} which generalizes the local well-posedness result in [1]. We also establish the ill-posedness result of the generalized Camassa-Holm equation and give a blow-up criterion.

引用

页码：1358 / 1381

页数：24

共 43 条

[1]

[Anonymous], 2011, FOURIER ANAL NONLINE

[2] INITIAL-VALUE PROBLEM FOR KORTEWEG-DEVRIES EQUATION [J].

BONA, JL ;

SMITH, R .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1975, 278 (1287) :555-601

[3] Global dissipative solutions of the Camassa-Holm equation [J].

Bressan, Alberto ;

Constantin, Adrian .

ANALYSIS AND APPLICATIONS, 2007, 5 (01) :1-27

[4] Global conservative solutions of the Camassa-Holm equation [J].

Bressan, Alberto ;

Constantin, Adrian .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 183 (02) :215-239

[5] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[6]

Chemin J.-Y., 2004, CRM series, V1, P53

[7]

Constantin A, 2000, COMMUN PUR APPL MATH, V53, P603

[8] On the cauchy problem for the periodic Camassa-Holm equation [J].

Constantin, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 141 (02) :218-235

[9]

Constantin A, 1998, COMMUN PUR APPL MATH, V51, P475, DOI 10.1002/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO

[10]

2-5

← 1 2 3 4 5 →