  In this article we prove highly improved and flexible Strichartz-type
estimates allowing us to generalize the asymptotics we obtained for a
stratified and rotating incompressible Navier-Stokes system: for large (and
less regular) initial data, we obtain global well-posedness, asymptotics (as
the Rossby number $\epsilon$ goes to zero) and convergence rates as a power of
the small parameter $\epsilon$. Our approach is lead by the special structure
of the limit system: the 3D quasi-geostrophic system.
