LOCAL WELL-POSEDNESS AND PERSISTENCE PROPERTY FOR THE GENERALIZED NOVIKOV EQUATION

被引：8
|
作者：
Zhao, Yongye [1 ]
Li, Yongsheng [1 ]
Yan, Wei [2 ]
机构：
[1] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
[2] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 02期
关键词：
Cauchy problem; persistence property; Novikov equation; Besov spaces; Littlewood-Paley decomposition; CAMASSA-HOLM EQUATION; DEGASPERIS-PROCESI EQUATION; SHALLOW-WATER EQUATION; BLOW-UP PHENOMENA; PERIODIC INTEGRABLE EQUATION; INFINITE PROPAGATION SPEED; CAUCHY-PROBLEM; GLOBAL EXISTENCE; PEAKON SOLUTIONS; WEAK SOLUTIONS;
D O I：
10.3934/dcds.2014.34.803
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the generalized Novikov equation which describes the motion of shallow water waves. By using the Littlewood-Paley decomposition and nonhomogeneous Besov spaces, we prove that the Cauchy problem for the generalized Novikov equation is locally well-posed in Besov space B-p,r(s) with 1 <= p,r <= +infinity and s > max {1 + 1/p, 3/2}. We also show the persistence property of the strong solutions which implies that the solution decays at infinity in the spatial variable provided that the initial function does.
引用
收藏
页码：803 / 820
页数：18
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