A note on the Cauchy problem of the Novikov equation

被引：63
|
作者：
Wu, Xinglong [1 ]
Yin, Zhaoyang [1 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
来源：
APPLICABLE ANALYSIS | 2013年 / 92卷 / 06期
关键词：
the Novikov equation; local well-posedness; ill-posedness; Besov spaces; lower semicontinuity; peakon solutions; 35G25; 35L05; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; INTEGRABLE EQUATION; BREAKING WAVES; SHOCK-WAVES;
D O I：
10.1080/00036811.2011.649735
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we mainly study the Cauchy problem of the Novikov equation. We first establish local well-posedness of the equation in Besov space . Then we derive a lower bound for the maximal existence time and lower semicontinuity of the existence time. Finally, we prove that the equation is ill-posed in by peakon solutions which exist globally in time to the equation.
引用
收藏
页码：1116 / 1137
页数：22
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