# Scattering below the ground state for the 2$d$ radial nonlinear Schr\"odinger equation

## TL;DR

This paper provides a new, simplified proof for scattering of radial solutions below the ground state threshold in the 2D focusing nonlinear Schrödinger equation, using localized virial/Morawetz estimates.

## Contribution

It introduces a straightforward proof approach for radial initial data, leveraging localized virial/Morawetz estimates to handle error terms.

## Key findings

- Proves scattering below the ground state in 2D focusing NLS for radial data.
- Utilizes localized virial/Morawetz estimates to control error terms.
- Simplifies previous proofs for this scattering regime.

## Abstract

We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schr\"odinger equation in two space dimensions. We present a simple new proof that treats the case of radial initial data. The key ingredient is a localized virial/Morawetz estimate; the radial assumption aids in controlling the error terms resulting from the spatial localization.