Sharper dispersive estimates and asymptotics for a Boussinesq-type system with larger ill-prepared initial data

Article type: Research Article

Authors: Charve, Frédéric^{; *}

Affiliations: Univ Paris Est Creteil, CNRS, LAMA, F-94010 Creteil, 2 Univ Gustave Eiffel, LAMA, F-77447 Marne-la-Vallée, France

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: The aim of this article is to extend previous works about the asymptotics of an ill-prepared fast rotating, highly stratified incompressible Navier–Stokes system. Thanks to improved Strichartz and a priori estimates, we are able not only to cover a case which was unanswered in our previous work (allowing bigger ill-prepared initial data) but also to improve the convergence rates and reduce some assumptions on the initial data. In passing we also widen the range of some parameters and compare two methods to obtain dispersive estimates.

Keywords: Stratified rotating Navier-Stokes system, 3-dimensional quasi-geostrophic system, Strichartz estimates, Besov spaces

DOI: 10.3233/ASY-221777

Journal: Asymptotic Analysis, vol. 131, no. 3-4, pp. 443-470, 2023