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

Frederic Charve (1)

1 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

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.

Mots clés: MSC: 35Q35; 35Q86; 35B40; 76D50; 76U05 Geophysical incompressible fluids; Strichartz estimates; Besov and Sobolev spaces

Domaines: Equations aux dérivées partielles [math.AP]

Frederic Charve. Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces. Tunisian Journal of Mathematics, 2023, 5 (1), pp.171-213. ⟨10.2140/tunis.2023.5.171⟩. ⟨hal-03636542v2⟩