Article ID Journal Published Year Pages File Type
4664064 Acta Mathematica Scientia 2012 7 Pages PDF
Abstract

In this article, we consider the Cauchy problems for the modified Kawahara equation∂tu+μ∂x(u3)+α∂x3u+β∂x3u+γ∂xu=0and the Kaup-Kupershmidt equation∂tu+μu∂x2u+α∂x5u+β∂x3u+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<−14 and that the Kaup-Kupershmidt equation is ill-posed for the initial data in Hs(R) with s < 0.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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