ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

doi:10.1016/S0252-9602(12)60050-2

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 710-716.doi: 10.1016/S0252-9602(12)60050-2

ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

闫威|李用声

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

收稿日期:2010-03-20 出版日期:2012-03-20 发布日期:2012-03-20
基金资助:
This work is supported by NNSFC under grant numbers 10771074 and 11171116; Yan is also supported in part by NNSFC under grant number 10801055 and the Doctoral Program of NEM of China under grant number 200805611026; Li is also supported in part by the Fundamental Research Funds for the Central Universities under the grant number 2012ZZ0072.

ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

YAN Wei, LI Yong-Sheng

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received:2010-03-20 Online:2012-03-20 Published:2012-03-20
Supported by:
This work is supported by NNSFC under grant numbers 10771074 and 11171116; Yan is also supported in part by NNSFC under grant number 10801055 and the Doctoral Program of NEM of China under grant number 200805611026; Li is also supported in part by the Fundamental Research Funds for the Central Universities under the grant number 2012ZZ0072.

摘要/Abstract

摘要：

In this article, we consider the Cauchy problems for the modified Kawahara
equation
∂_tu +μ∂_x(u³) + α∂⁵_xu + β∂³_xu + γ∂_xu = 0
and the Kaup-Kupershmidt equation
∂_tu + μu∂²_xu + α∂⁵_xu + β∂³_xu + γ∂_xu = 0.
Using the general well-posedness principle introduced by I. Bejenaru and T. Tao, we prove that the modified Kawahara equation is ill-posed for the initial data in Hs(R) with s < −1/4 and that the Kaup-Kupershmidt equation is ill-posed for the initial data in H^s(R) with
s < 0.

关键词: Ill-posedness, modified Kawahara equation, Kaup-Kupershmidt equation, general well-posedness principle

Abstract:

Key words: Ill-posedness, modified Kawahara equation, Kaup-Kupershmidt equation, general well-posedness principle

中图分类号:

35E15

闫威, 李用声. ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION[J]. 数学物理学报(英文版), 2012, 32(2): 710-716.

YAN Wei, LI Yong-Sheng. ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION[J]. Acta mathematica scientia,Series B, 2012, 32(2): 710-716.

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ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

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