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

TL;DR

This paper investigates the lifespan and asymptotic behavior of rotating and stratified fluid systems with large, ill-prepared initial data in critical spaces, providing simplified proofs and explicit convergence rates.

Contribution

It introduces a simplified, adaptable proof for analyzing primitive systems with ill-prepared data, extending to rotating fluids with explicit convergence rates.

Findings

Extended analysis to rotating fluids with large initial data

Provided explicit convergence rates for the asymptotics

Simplified proof techniques for complex fluid systems

Abstract

In this article 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 2D horizontal part and a very large 3D part. We also provide explicit convergence rates.