  Bose-Einstein condensation is usually modeled by nonlinear Schroedinger
equations with harmonic potential. We study the Cauchy problem for these
equations. We show that the local problem can be treated as in the case with no
potential. For the global problem, we establish an evolution law, which is the
analogue of the pseudo-conformal conservation law for the nonlinear
Schroedinger equation. With this evolution law, we give wave collapse criteria,
as well as an upper bound for the blow up time. Taking the physical scales into
account, we finally give a lower bound for the blow up time.
