We study the lifespan and asymptotics (in the large rotation and stratification
regime) for the primitive system for highly ill-prepared initial data in critical spaces.
Compared to our previous works, we simplified the proof and made it adaptable to
the rotating fluids system with highly ill-prepared initial data decomposed as a sum
of a 2D horizontal part and a very large 3D part. We also provide explicit
convergence rates.
