Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation

We study the initial value problem for the defocusing nonlinear wave equation with cubic nonlinearity F(u)=|u|^2u in the energy-supercritical regime, that is dimensions d\geq 5. We prove that solutions to this equation satisfying an a priori bound in the critical homogeneous Sobolev space exist globally in time and scatter in the case of spatial dimensions d\geq 6 with general (possibly non-radial) initial data, and in the case of spatial dimension d=5 with radial initial data.