Scattering for the quadratic beam equation with radial initial data

Abstract

In this paper, we prove scattering for the beam equation with quadratic nonlinear term assuming that the initial data is radial and below some thresholds with the spatial dimensions 8≤d≤11. The main difficult part is the so-called mass critical case for d=8. We use the method of Dodson-Murphy [7] without concentration-compactness argument to obtain scattering.