## Differential and Integral Equations

### Scattering for the critical 2-D NLS with exponential growth

#### Abstract

In this article, we establish in the radial framework the $H^1$-scattering for the critical 2-D nonlinear Schrödinger equation with exponential growth. Our strategy relies on both the a priori estimate derived in [10, 23] and the characterization of the lack of compactness of the Sobolev embedding of $H_{rad}^1(\mathbb R^2)$ into the critical Orlicz space ${\mathcal L}(\mathbb R^2)$ settled in [4]. The radial setting, and particularly the fact that we deal with bounded functions far away from the origin, occurs in a crucial way in our approach.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 3/4 (2014), 233-268.

Dates
First available in Project Euclid: 30 January 2014