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

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.

arXiv commentUpdate. 25 pages