Energy scattering for radial focusing inhomogeneous bi-harmonic Schr\"odinger equations

Abstract

This note studies the asymptotic behavior of global solutions to the fourth-order Schr\"odinger equation $$i\dot u+\Delta^2 u+F(x,u)=0 .$$ Indeed, for both cases, local and non-local source term, the scattering is obtained in the focusing mass super-critical and energy sub-critical regimes, with radial setting. This work uses a new approach due to Dodson-Murphy \cite{dm}.