We obtain, for a stratified, rotating, incompressible Navier–Stokes system, generalized asymptotics as
the Rossby number
goes to zero (without assumptions on the diffusion coefficients). For
ill-prepared, less regular initial data with large blowing-up norm in terms of
, we
show global well-posedness and improved convergence rates (as a power of
)
towards the solution of the limit system, called the 3-dimensional quasigeostrophic
system. Aiming for significant improvements required us to avoid as much as possible
resorting to classical energy estimates involving oscillations. Our approach relies on
the use of structures and symmetries of the limit system, and of highly improved
Strichartz-type estimates.
