Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

被引：561
|
作者：
Li, YA [1 ]
Olver, PJ [1 ]
机构：
[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2000年 / 162卷 / 01期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1006/jdeq.1999.3683
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish local well-posedness in the Sobolev space H-s with any s > 3/2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa-Holm equation. However, unlike the more familiar Korteweg-de Vries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions. (C) 2000 Academic Press.
引用
收藏
页码：27 / 63
页数：37
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