THE CAUCHY PROBLEM FOR THE CAMASSA-HOLM-NOVIKOV EQUATION  

作　　者：朱铭旋 姜在红 Mingxuan ZHU;Zaihong JIANG(School of Mathematical Sciences,Qufu Normal University,Qufu 273100,China;Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]School of Mathematical Sciences,Qufu Normal University,Qufu 273100,China [2]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Acta Mathematica Scientia》2023年第2期736-750,共15页数学物理学报（B辑英文版）

基　　金：partially supported by the National Natural Science Foundation of China(12071439);the Zhejiang Provincial Natural Science Foundation of China(LY19A010016);the Natural Science Foundation of Jiangxi Province(20212BAB201016)。

摘　　要：In this paper,we consider the Cauchy problem for the Camassa-Holm-Novikov equation.First,we establish the local well-posedness and the blow-up scenario.Second,infinite propagation speed is obtained as the nontrivial solution u(x,t)does not have compact x-support for any t>0 in its lifespan,although the corresponding u0(x)is compactly supported.Then,the global existence and large time behavior for the support of the momentum density are considered.Finally,we study the persistence property of the solution in weighted Sobolev spaces.

关 键 词：Camassa-Holm-Novikov equation local well-posedness blow-up scenario in-finite propagation speed global existence large time behavior persistence property 

分 类 号：O175[理学—数学]