Low-regularity global well-posedness for the defocusing cubic wave equation outside a ball with radial initial data

We study the three-dimensional defocusing cubic nonlinear wave equation with homogeneous Dirichlet boundary condition in the exterior of the unit ball, $Ω=\R^3\backslash\overline{B(0,1)}$, for radial initial data. For every $\frac12\leq s\leq\frac34$, we establish global well-posedness in $\dot H^s_