The radial defocusing energy-supercritical cubic nonlinear wave equation in ℝ\u3csup\u3e1+5\u3c/sup\u3e

In this work, we establish a frequency localized version of the classical Morawetz inequality adapted to almost periodic solutions of the defocusing cubic nonlinear wave equation in dimension d = 5. As an application, we conclude that radial solutions to this equation that remain bounded in the critical homogeneous Sobolev space exist globally in time and scatter. © 2014 IOP Publishing Ltd & London Mathematical Society