Global well-posedness and scattering for the radial, defocusing, cubic nonlinear wave equation

Abstract

In this paper we prove global well-posedness and scattering for the defocusing, cubic, nonlinear wave equation on ${\mathbf{R}}^{1+3}$ with radial initial data lying in the critical Sobolev space ${\dot{H}}^{1/2}({\mathbf{R}}^3)\times {\dot{H}}^{-1/2}({\mathbf{R}}^3)$.