  We prove that no finite time blow up can occur for nonlinear Schroedinger
equations with quadratic potentials, provided that the potential has a
sufficiently strong repulsive component. This is not obvious in general, since
the energy associated to the linear equation is not positive. The proof relies
essentially on two arguments: global in time Strichartz estimates, and a
refined analysis of the linear equation, which makes it possible to use
continuity arguments and to control the nonlinear effects.
