THE DEFOCUSING ENERGY-SUPERCRITICAL CUBIC NONLINEAR WAVE EQUATION IN DIMENSION FIVE

We consider the energy-supercritical nonlinear wave equation u(tt)-Delta u + broken vertical bar u broken vertical bar(2)u = 0 with defocusing cubic nonlinearity in dimension d = 5 with no radial assumption on the initial data. We prove that a uniform-in-time a priori bound on the critical norm implies that solutions exist globally in time and scatter at infinity in both time directions. Together with our earlier works in dimensions d >= 6 with general data and dimension d = 5 with radial data, the present work completes the study of global well-posedness and scattering in the energy-supercritical regime for the cubic nonlinearity under the assumption of uniform-in-time control over the critical norm.