The Cauchy problem for the integrable Novikov equation

被引：95
|
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
收藏
页码：298 / 318
页数：21
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