Ill-posedness of Kawahara equation and Kaup–Kupershmidt equation

In this paper we consider the Cauchy problems for the Kawahara equation and the Kaup–Kupershmidt equation. By using the general well-posedness principle introduced by I. Bejenaru and T. Tao (2006) [1], we prove that the Kawahara equation is ill-posed for the initial data in H s ( R ) with s < − 9 4 and the Kaup–Kupershmidt equation is ill-posed for the initial data in H s ( R ) with s < − 1 4 .