  We prove bilinear estimates for the Schr\"odinger equation on 3D domains,
with Dirichlet boundary conditions. On non-trapping domains, they match the
$\mathbb{R}^3$ case, while on bounded domains they match the generic boundary
less manifold case. As an application, we obtain global well-posedness for the
defocusing cubic NLS for data in $H^s_0(\Omega)$, $1<s\leq 3$, with $\Omega$
any bounded domain with smooth boundary.
