# Enhanced convergence rates and asymptotics for a dispersive Boussinesq-type system with large ill-prepared data

## TL;DR

This paper develops advanced Strichartz estimates to analyze a dispersive Boussinesq-type system, enabling the authors to establish global well-posedness, asymptotic behavior, and convergence rates for large, less regular initial data as the Rossby number approaches zero.

## Contribution

It introduces improved Strichartz estimates and applies them to derive new asymptotics and convergence results for a dispersive Boussinesq-type system with large initial data.

## Key findings

- Global well-posedness for large initial data
- Asymptotic behavior as Rossby number tends to zero
- Quantitative convergence rates based on small parameter epsilon

## Abstract

In this article we prove highly improved and flexible Strichartz-type estimates allowing us to generalize the asymptotics we obtained for a stratified and rotating incompressible Navier-Stokes system: for large (and less regular) initial data, we obtain global well-posedness, asymptotics (as the Rossby number $\epsilon$ goes to zero) and convergence rates as a power of the small parameter $\epsilon$. Our approach is lead by the special structure of the limit system: the 3D quasi-geostrophic system.