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

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