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

TL;DR

This paper improves dispersive estimates and asymptotic analysis for a Boussinesq-type system with larger ill-prepared initial data, extending previous results by leveraging enhanced Strichartz estimates.

Contribution

It introduces improved Strichartz estimates that allow handling larger ill-prepared initial data and relaxes previous assumptions on initial conditions.

Findings

Extended asymptotic results for larger initial data

Reduced restrictions on initial data assumptions

Compared methods for dispersive estimates

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 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 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.