Scattering threshold for radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in $d\ge 5$

Abstract

We extend the scattering result for the radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in $d\le 4$ given by Cheng et al. to the case $d\ge 5$. The main ingredient is a suitable long time perturbation theory which is applicable for $d\ge 5$. The paper will therefore give a full characterization on the scattering threshold for the radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation in all dimensions $d\ge 3$.

Simplified version with only the stability result. More details are found in v1

References in corpus (1)

• Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case