# Scattering above energy norm of a focusing size-dependent log energy-supercritical Schrodinger equation with radial data below ground state

## TL;DR

This paper proves scattering for radial solutions of a focusing size-dependent log energy-supercritical Schrödinger equation below ground state energies in dimensions 3 to 5, extending understanding of critical energy thresholds.

## Contribution

It establishes scattering results for a class of focusing supercritical Schrödinger equations with size-dependent and log energy terms, below ground state energies, for radial data.

## Key findings

- Proves scattering for solutions below ground state energy levels.
- Extends scattering theory to size-dependent, log energy-supercritical regimes.
- Addresses dimensions 3, 4, and 5 with specific conditions on k.

## Abstract

Given $n \in \{ 3,4,5 \}$ and $k > 1$ (resp. $\frac{4}{3} > k > 1$) if $n \in \{ 3,4 \}$ (resp. $n=5$), we prove scattering of the radial $\tilde{H}^{k}:= \dot{H}^{k}(\mathbb{R}^{n}) \cap \dot{H}^{1}(\mathbb{R}^{n})$ solutions of a focusing size-dependent log energy-supercritical Schrodinger equation for critical energies below that of the ground states, and for critical potential energies below that of the ground states.