The Cauchy problem for the integrable Novikov equation

被引：94

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：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 253卷 / 01期

关键词：

Cauchy problem; Novikov equation; Besov spaces; WELL-POSEDNESS; BESOV-SPACES;

D O I：

10.1016/j.jde.2012.03.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the Cauchy problem for the integrable Novikov equation. By using the Littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the integrable Novikov equation is locally well-posed in the Besov space B-p.r(s), with 1 <= p, r + infinity and s > max{1 + 1/p, 3/2} In particular, when u(0) is an element of B-p.r(s) boolean AND H-l with 1 <= p, r <= +infinity and s > max{1 + 1/p, 3/2}, for all t is an element of [0, T], we have that vertical bar vertical bar u(t)vertical bar vertical bar H-l = vertical bar vertical bar u(0)vertical bar vertical bar(H)l. We also prove that the local well-posedness of the Cauchy problem for the Novikov equation fails in B-2.(3/2)(infinity). (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：298 / 318

页数：21

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