A new proof of scattering below the ground state for the non-radial focusing NLS

TL;DR

This paper provides a simplified proof of scattering for the non-radial focusing NLS below the ground state in dimensions three and higher, using an interaction Morawetz inequality instead of concentration compactness.

Contribution

It introduces a new approach to prove scattering without relying on concentration compactness, simplifying the existing proof for non-radial cases.

Findings

Established scattering below the ground state in higher dimensions

Developed an interaction Morawetz inequality for the problem

Provided a more straightforward proof method

Abstract

We revisit the scattering result of Duyckaerts, Holmer, and Roudenko for the non-radial $\dot H^{1/2}$-critical focusing NLS. By proving an interaction Morawetz inequality, we give a simple proof of scattering below the ground state in dimensions $d\geq 3$ that avoids the use of concentration compactness.