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

Frédéric Charve

Vol. 5 (2023), No. 1, 171–213
Abstract

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.

Keywords
rotating fluids, primitive system, 3D quasigeostrophic system, Strichartz estimates, ill-prepared initial data, convergence rate estimates
Mathematical Subject Classification
Primary: 35Q35
Secondary: 35B40, 35Q86, 76D50, 76U05
Milestones
Received: 10 April 2022
Accepted: 13 September 2022
Published: 20 April 2023
Authors
Frédéric Charve
LAMA (UMR 8050)
Université Paris-Est Créteil
Créteil
France