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In this paper we study the defocusing, cubic nonlinear wave equation in threedimensions with radial initial data. The critical space is $\dot{H}^{1/2}\times \dot{H}^{-1/2}$. We show that if the initial data is radial and lies in$(\dot{H}^{s} \times \dot{H}^{s - 1}) \cap (\dot{H}^{1/2} \times\dot{H}^{-1/2})$ for some $s > \frac{1}{2}$, then the cubic initial valueproblem is globally well - posed. We use the I - method and the long timeStrichartz estimates. This method is quite similar to the method used in [D2].

Global well - posedness for the defocusing, cubic, nonlinear wave  equation in three dimensions for radial initial in $\dot{H}^{s} \times  \dot{H}^{s - 1}$, $s > \frac{1}{2}$