## Differential and Integral Equations

### A new proof of long-range scattering for critical nonlinear Schrödinger equations

#### Abstract

We present a new proof of global existence and long range scattering, from small initial data, for the one--dimensional cubic gauge invariant nonlinear Schrödinger equation, and for Hartree equations in dimension $n \geq 2$. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi, and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument.

#### Article information

Source
Differential Integral Equations, Volume 24, Number 9/10 (2011), 923-940.

Dates
First available in Project Euclid: 20 December 2012