Mathematical Research Letters

Volume 25 (2018)

Number 6

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

Pages: 1805 – 1825



Benjamin Dodson (Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A.)

Jason Murphy (Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Mo., U.S.A.)


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.

Received 4 January 2018

Accepted 12 June 2018

Published 25 March 2019