μ-b方程族柯西问题的不适定性  

Ill-posedness of the Cauchy problem for theμ-b family

作　　者：严可欣 陈涵[1] 付英 Yan Kexin;Chen Han;Fu Ying(School of Mathematics and Statistic,Ningbo University,Ningbo 315211,China;School of Mathematics,Northwest University,Xi'an 710127,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211 [2]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2022年第4期494-503,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11631007);浙江省自然科学基金(LY22A010005).

摘　　要：研究了μ-b方程族的柯西问题在索伯列夫空间Hs(S)中的不适定性,该方程族可视为μ-Camassa-Holm方程和μ-Degasperis-Procesi方程的一个混合方程.通过构建对称的2-尖峰孤子解,并结合时间趋于生命周期时,解的Hs-范数极限的等价估计,证明了b和s满足一定范围时,μ-b方程族在索伯列夫空间Hs(S)中是不适定的.This paper discusses ill-posedness of the Cauchy problem for theμ-b family in the Sobolev spaces Hs(S),in which theμ-b family can be regarded as a mixed equation of theμ-Camassa-Holm equation andμ-Degasperis-Procesi equation.By constructing a symmetric 2-peakon solution and combining with the equivalent estimate of the Hs-norm of the solution as time tends to the lifespan,it is proved that theμ-b family is ill-posed in the Sobolev spaces Hs(S)when b and s satisfy a certain range.

关 键 词：μ-b方程族 μ-Camassa-Holm方程 μ-Degasperis-Procesi方程 不适定性 尖峰孤子解 

分 类 号：O178[理学—数学]