在本文中首先介绍了2D，3D不可压Euler方程的一些基本性质； 然后在不借助涡度的前提下仅用经典的能量方法对Euler方程进行探究，分别得出了在2D和3D情况下解的唯一性； 接着运用磨光函数和Hodge分解构造出了一族正则化方程，通过对正则化方程的研究，给出了Euler方程局部解的存在性； 最后说明如果局部解在任意时刻，它的$H^m$范数都能被控制，那么这个局部解就可以延拓到全局.

In this article,some fundamental properties of the 2D and 3D Euler equations are been showed at first. Then we get the uniqueness of smooth solutions of the 2D and 3D Euler equations by only using the energy methods. Next,we get the Local-in-Time existence of the Euler equations by studying the regularization of the Euler equations, which is derived from the mollifiers and Leray's projection operator.Finally,we find that the Local-in-Time solution of the Euler equations can be continued in time to get a global solution if the $H^m$ norm of the solution can be controlled.