  We prove modified Strichartz estimates on the one-dimensional torus, that are
adapted to a fourth-order dispersion relation, and use them to show global
well-posedness of nonlinear fourth-order Schr\"odinger equations. This extends
the (low regularity) existence theory of the adiabatic transition of the
Quantum Zakharov system to NLS. We show that the solutions behave continuously
with respect to the quantum parameter in every compact time interval. Globally
in time, however, we also show that such continuous dependence is generally not
uniform.
