Global well-posedness for the periodic Novikov equation with cubic nonlinearity

被引：6

作者：

Wu, Xinglong ^{[1
]}

Guo, Boling ^{[2
]}

机构：

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

来源：

APPLICABLE ANALYSIS | 2016年 / 95卷 / 02期

基金：

中国国家自然科学基金;

关键词：

the periodic Novikov equation; well-posedness; blow-up scenario; conservation laws; global solutions; Peakon solutions; INTEGRABLE EQUATION; WEAK SOLUTIONS; SHOCK-WAVES; BREAKING;

D O I：

10.1080/00036811.2015.1005611

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of the Cauchy problem to the periodic Novikov equation. Firstly, the local well-posedness for the equation is established. Secondly, we give the precise blow-up criterion, conservation laws, and prove that the equation has global strong solutions in time, if the initial potential does not change sign on R. Thirdly, with the initial potential satisfying the sign conditions, we show the existence of global weak solutions in time. Moreover, the uniqueness of global solution is addressed.

引用

页码：405 / 425

页数：21

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