On large future-global-in-time solutions to energy-supercritical nonlinear wave equation

In a recent work we constructed future-global-in-time large solution to the Cauchy problem for semi-linear wave equation on R3+1 with nonlinear terms satisfying the null conditions. In this article we show that the method also applies to energy-supercritical nonlinear wave equation with power type nonlinearity. In addition to constructing a large global-in-time solution, we also show that the solution constructed decays to zero as t ->infinity.