Global well-posedness and scattering for the defocusing cubic NLS in four dimensions

TL;DR

This paper offers a new proof for the global well-posedness and scattering of the defocusing energy-critical nonlinear Schrödinger equation in four dimensions, building on recent advances in related NLS problems.

Contribution

It provides an alternative proof inspired by Dodson's work, simplifying or extending previous results on the energy-critical NLS in four dimensions.

Findings

Established global well-posedness for the defocusing cubic NLS in 4D

Proved scattering behavior for solutions in this setting

Introduced a proof technique inspired by mass-critical NLS work

Abstract

In this short note we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical NLS in four space dimensions obtained previously by Ryckman and Visan. The argument is inspired by the recent work of Dodson on the mass-critical NLS.