Scattering for the defocusing, cubic nonlinear Schr{\"o}dinger equation with initial data in a critical space

TL;DR

This paper proves that solutions to the defocusing cubic nonlinear Schrödinger equation scatter when initial data is in a critical Besov space, and provides polynomial bounds on the scattering size related to the initial data norm.

Contribution

It establishes scattering results for the equation with initial data in a critical Besov space, extending previous results to this function space setting.

Findings

Proves scattering for initial data in a critical Besov space.

Provides polynomial bounds on the scattering size based on initial data norm.

Extends scattering theory to a broader class of initial data spaces.

Abstract

In this note we prove scattering for a defocusing nonlinear Schr{\"o}dinger equation with initial data lying in a critical Besov space. In addition, we obtain polynomial bounds on the scattering size as a function of the critical Besov norm.