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

页码：27 / 63

页数：37

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