On the global Cauchy problem for the nonlinear Schrödinger equation

We mainly survey recent results on the nonlinear Schrödinger equations with special emphasis on the Cauchy problem, local and global in time and for various regularity assumptions on the initial data.

本文主要综述了非线性薛定谔方程（nonlinear Schrödinger equations）的近期研究进展，重点聚焦于柯西问题（Cauchy problem）、时间局部与全局解，以及初值的各类正则性假设相关研究。