The radial defocusing energy-supercritical cubic nonlinear wave equation   in R^{1+5}
  In this work, we consider the energy-supercritical defocusing cubic nonlinear wave equation in dimension d=5 for radially symmetric initial data. We prove that an a priori bound in the critical space implies global well-posedness and scattering. The main tool that we use is a frequency localized version of the classical Morawetz inequality, inspired by recent developments in the study of the mass and energy critical nonlinear Schr\"odinger equation. 
Aynur Bulut
math.AP