中山大学学报(自然科学版)
中山大學學報(自然科學版)
중산대학학보(자연과학판)
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS SUNYATSENI
2014年
4期
8-12
,共5页
张双虎%冯兆永%杨凯波
張雙虎%馮兆永%楊凱波
장쌍호%풍조영%양개파
修正CamassaHolm 方程%爆破%关于初值非一致依赖性
脩正CamassaHolm 方程%爆破%關于初值非一緻依賴性
수정CamassaHolm 방정%폭파%관우초치비일치의뢰성
the modified Camassa-Holm equation%blow up%non-uniform dependence on initial data
主要研究修正Camassa-Holm方程的Cauchy问题。首先提出了一个新的爆破结果,这一结果优化了早先获得的一些结果;然后证明了修正 Camassa-Holm方程的Cauchy问题在解对初值不一致连续依赖意义下在空间Hs ( R),s <32中不适定。
主要研究脩正Camassa-Holm方程的Cauchy問題。首先提齣瞭一箇新的爆破結果,這一結果優化瞭早先穫得的一些結果;然後證明瞭脩正 Camassa-Holm方程的Cauchy問題在解對初值不一緻連續依賴意義下在空間Hs ( R),s <32中不適定。
주요연구수정Camassa-Holm방정적Cauchy문제。수선제출료일개신적폭파결과,저일결과우화료조선획득적일사결과;연후증명료수정 Camassa-Holm방정적Cauchy문제재해대초치불일치련속의뢰의의하재공간Hs ( R),s <32중불괄정。
The Cauchy problem of the modified Camassa-Holm equation is mainly studied .First, a new blow-up phenomenon which is an improvement of the earlier ones is presented .Then it is proved that the Cauchy problem for the modified Camassa-Holm equation is not locally well-posedness in the sense that its solution does not depend uniformly continuously on the initial data .