In this article, we consider the Cauchy problems for the modified Kawahara equationδtu＋μδx（u3）＋αδx5u＋βδx3u＋γδxu=0 and the Kaup-Kupershmidt equation δtu＋μuδx2u＋αδx5u＋βδx3u＋βδx3u＋γδxu=0Usi...In this article, we consider the Cauchy problems for the modified Kawahara equationδtu＋μδx（u3）＋αδx5u＋βδx3u＋γδxu=0 and the Kaup-Kupershmidt equation δtu＋μuδx2u＋αδx5u＋βδx3u＋βδx3u＋γδxu=0Using the general well-posedness principle introduced by I. Bejenaru and T. Tao, we prove 1 that the modified Kawahara equation is ill-posed for the initial data in H8 （It） with s 〈 - and that the Kaup-Kupershmidt equation is ill-posed for the initial data in HS（It） with s〈0.展开更多
基金supported by NNSFC under grant numbers 10771074 and 11171116supported in part by NNSFC under grant number 10801055+1 种基金the Doctoral Program of NEM of China under grant number 200805611026supported in part by the Fundamental Research Funds for the Central Universities under the grant number 2012ZZ0072
文摘In this article, we consider the Cauchy problems for the modified Kawahara equationδtu＋μδx（u3）＋αδx5u＋βδx3u＋γδxu=0 and the Kaup-Kupershmidt equation δtu＋μuδx2u＋αδx5u＋βδx3u＋βδx3u＋γδxu=0Using the general well-posedness principle introduced by I. Bejenaru and T. Tao, we prove 1 that the modified Kawahara equation is ill-posed for the initial data in H8 （It） with s 〈 - and that the Kaup-Kupershmidt equation is ill-posed for the initial data in HS（It） with s〈0.
