  We prove wellposedness of the Cauchy problem for the cubic nonlinear
Schrodinger equation with Dirichlet boundary conditions and radial data on 3D
balls. The main argument is based on a bilinear eigenfunction estimate and the
use of $X^{s,b}$ spaces. The last part presents a first attempt to study the
non radial case. We prove bilinear estimates for the linear Schrodinger flow
with particular initial data.
