中文摘要：

主要研究了高阶色散方程ut＋δ2j＋1xu=δj＋1x（u2）＋δj-1x（ux2）,j≥2,j∈N,x,t∈R的柯西问题.使用修正傅里叶限制范数方法和Strichartz估计以及修正Bourgain空间,证明了这个问题在修正的Sobolev空间H（s,1/2j）（s〉-j/2＋3/4）上是局部适定的.使用迭代技巧,

英文摘要：

In this paper,we consider the Cauchy problem for the higher-order dispersive equation ut＋δ2j＋1xu=δj＋1x（u2）＋δj-1x（u2x）,j≥2,j∈N,x,t∈R.By using the modified Fourier restriction norm method and Strichartz estimate and the modified Bourgain space,we prove that the problem is locally well-posed in modified Sobolev space H（s,1/2j） with s〉-j/2＋3/4.By using the iteration technique,we also prove that the flow map is not C2 at the origin if we assume that the problem is well-posed in H（s,w）with 0〈w〈12jfor any s∈R.