Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in <(H)over dot> x <(H)over dot>s-1, s > 1/2

In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is <(H)over dot>(1/2) x <(H)over dot>(-1/2) . We show that if the initial data is radial and lies in (<(H)over dot>(s) x <(H)over dot>(s-1)) boolean AND (<(H)over dot>(1/2) x <(H)over dot>(-1/2)) for some , then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11].