  We consider the defocusing, cubic nonlinear wave equation with zero Dirichlet
boundary value in the exterior $\Omega = \R^3\backslash \bar{ B}(0,1)$. We make
use of the distorted Fourier transform in \cite{LiSZ:NLS, Taylor:PDE:II} to
establish the dispersive estimate and the global-in-time (endpoint) Strichartz
estimate of the linear wave equation outside of the ball with radial data. As
an application, we combine the Fourier truncation method as those in
\cite{Bourgain98:FTM, GallPlan03:NLW, KenigPV00:NLW} with the energy method to
show global well-posedness of radial solution to the defoucusing, cubic
nonlinear wave equation outside of a ball in the Sobolev space $\left(\dot
H^{s}_{D}(\Omega) \cap L^4(\Omega) \right)\times \dot H^{s-1}_{D}(\Omega)$ with
$s>3/4$. To the best of the author's knowledge, it is first result about low
regularity of semilinear wave equation with zero Dirichlet boundary value on
the exterior domain.
