Acta mathematica scientia, Series B >
ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION
Received date: 2010-03-20
Online 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.
In this article, we consider the Cauchy problems for the modified Kawahara
equation
∂tu +μ∂x(u3) + α∂5xu + β∂3xu + γ∂xu = 0
and the Kaup-Kupershmidt equation
∂tu + μu∂2xu + α∂5xu + β∂3xu + 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 Hs(R) with
s < 0.
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 . DOI: 10.1016/S0252-9602(12)60050-2
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