The Cauchy problem for the Novikov equation

被引：57

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：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2013年 / 20卷 / 03期

关键词：

Cauchy problem; Novikov equation; Blow-up; WATER-WAVES; TRAJECTORIES; BREAKING;

D O I：

10.1007/s00030-012-0202-1

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 Novikov equation. We prove that the Cauchy problem for the Novikov equation is not locally well-posed in the Sobolev spaces with in the sense that its solutions do not depend uniformly continuously on the initial data. Since the Cauchy problem for the Novikov equation is locally well-posed in with s > 3/2 in the sense of Hadamard, our result implies that s = 3/2 is the critical Sobolev index for well-posedness. We also present two blow-up results of strong solution to the Cauchy problem for the Novikov equation in with s > 3/2.

引用

页码：1157 / 1169

页数：13

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