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In this article we study the lifespan and asymptotics (in the large rotationand stratification regime) for the Primitive system for highly ill-preparedinitial data in critical spaces. Compared to our previous works, we simplifiedthe proof and made it adaptable to the Rotating fluids system with highlyill-prepared initial data decomposed as a sum of 2D horizontal part and a verylarge 3D part. We also provide explicit convergence rates.

Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces