Scattering threshold for radial defocusing-focusing mass-energy double critical nonlinear Schr\"odinger equation in $d\geq 5$

TL;DR

This paper extends the understanding of scattering phenomena for the radial defocusing-focusing mass-energy double critical nonlinear Schrödinger equation to higher dimensions, providing a comprehensive characterization of the scattering threshold for all dimensions $d\,\geq\,3$.

Contribution

It introduces a suitable long time perturbation theory applicable for $d\geq 5$, enabling the extension of scattering results to higher dimensions.

Findings

Established scattering results for $d\geq 5$

Provided a full characterization of the scattering threshold in all $d\geq 3$

Developed a new long time perturbation theory

Abstract

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