Rotation-Camassa-Holm方程的波破准则
Wave-breaking criterion for the Rotation-Camassa-Holm equation
胡凤伟 1魏龙1
作者信息
- 1. 杭州电子科技大学理学院,浙江杭州 310018
- 折叠
摘要
研究Rotation-Camassa-Holm(R-CH)方程的解在空间Hs(R)中的波破准则.首先运用特征线法、Young不等式、Sobolev不等式以及守恒量等得到一个Riccati型不等式;然后借助已有的对Riccati型不等式的研究,得到解发生波破的判别标准,即给定一个初值条件使得方程的解在有限时间内发生波破.
Abstract
A wave-breaking criterion for the Rotation-Camassa-Holm(R-CH)equation is studied in Sobolev space Hs(R).Firstly,we derive a Riccati-type inequality by the Lagrange flow,Young's inequality,Sobolev inequality and conserved quantity.Then,by using the relevant results of the analysis of Riccati type inequality,a wave breaking criterion for the R-CH equation is obtained,i.e.,an initial condition that causes the solution of the equation to lead to wave breaking within a finite time.
关键词
Rotation-Camassa-Holm方程/波破/Riccati型不等式Key words
Rotation-Camassa-Holm equation/blow-up/Riccati-type inequality引用本文复制引用
基金项目
浙江省自然科学基金资助项目(LY21A010008)
出版年
2024
NETL
NSTL
万方数据