Dynamics of subcritical threshold solutions for the 4d energy-critical NLS

Abstract

We study dynamics of the 4$d$ energy-critical nonlinear Schrödinger equation at the ground state energy. Previously, Duyckaerts and Merle [Geom. Funct. Anal. (2009)] proved that any radial solution with kinetic energy less than that of the ground state either scatters in both time directions or coincides (modulo symmetries) with a heteroclinic orbit, which scatters in one time direction and converges to the ground state in the other. We extend this result to the non-radial setting.

35 pages