The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation

被引：65

作者：

Lai, Shaoyong ^{[1
]}

Wu, Yonghong ^{[2
]}

机构：

[1] SW Univ Finance & Econ, Dept Appl Math, Chengdu 610074, Peoples R China

[2] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 248卷 / 08期

关键词：

Local well-posedness; Weak solution; Generalized Camassa-Holm equation; High order nonlinear terms; Pseudoparabolic regularization method; SHALLOW-WATER EQUATION; SOLITARY WAVE SOLUTIONS; GEODESIC-FLOW; STABILITY; WELLPOSEDNESS; TRAJECTORIES; BREAKING; SOLITONS; COMPACT; PEAKONS;

D O I：

10.1016/j.jde.2010.01.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A generalization of the Camassa-Holm equation, a model for shallow water waves, is investigated Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space H(s)(R) with s > 2 is established via a limiting procedure In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space H(s) with 1 < s <= 3/2 Is developed (C) 2010 Elsevier Inc All rights reserved

引用

页码：2038 / 2063

页数：26

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