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The paper deals with the defocusing case of the energy subcritical non-linearwave equation in $R^3$. We assume the initial data is in the space $\dot{H}^s\times \dot{H}^{s-1}$ and radial. If $s=1$, this is the energy space and thescattering results are known. In this paper we choose $15/16<s<1$ and assumethat the nonlinearity equals $-|u|^p u$ with $p = 2/{3/2 -s}$, so that thisproblem is $\dot{H}^s \times \dot{H}^{s-1}$ critical. We will prove the globalwell-posedness and scattering of the solution under the additional assumptionthat the $\dot{H}^s \times \dot{H}^{s-1}$ norm of the solution is uniformlybounded for all time $t$ in the maximal lifespan of the solution.

Global Well-posedness and Scattering of Defocusing Energy subcritical Nonlinear Wave Equation in dimension 3 with radial data