Rotation-Camassa-Holm方程的波破准则  

Wave-breaking criterion for the Rotation-Camassa-Holm equation

作　　者：胡凤伟 魏龙[1] HU Fengwei;WEI Long(school of sciences,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2024年第3期79-83,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：浙江省自然科学基金资助项目(LY21A010008)。

摘　　要：研究Rotation-Camassa-Holm(R-CH)方程的解在空间H~s(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。A wave-breaking criterion for the Rotation-Camassa-Holm(R-CH)equation is studied in Sobolev space H'(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 

分 类 号：O175.2[理学—数学]