Scattering for the radial defocusing cubic nonlinear wave equation with initial data in the critical Sobolev space

Abstract

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 ${\dot{H}}^{1∕2}({\mathbf{R}}^3)\times {\dot{H}}^{-1∕2}({\mathbf{R}}^3)$. This result is sharp for radial initial data.