# Global existence and convergence for non-dimensionalized incompressible Navier-Stokes equations in low Froude number regime

## TL;DR

This paper establishes global existence and convergence results for density-dependent incompressible Navier-Stokes equations in a low Froude number regime, showing convergence to a 2D stratified system without small initial data assumptions.

## Contribution

It proves global well-posedness and convergence of the density-dependent Navier-Stokes equations in the low Froude number limit, with no smallness condition on initial data.

## Key findings

- Global well-posedness in low Froude regime
- Strong convergence to 2D stratified Navier-Stokes system as Froude number tends to zero
- No small initial data assumption required

## Abstract

We prove that the incompressible, density dependent, Navier-Stokes equations are globally well posed in a low Froude number regime. The density is supposed to be increasing in depth and linearized around a stable state. Moreover if the Froude number tends to zero we prove that such system converges (strongly) to a two-dimensional, stratified Navier-Stokes system with full diffusivity. No smallness assumption is made on the initial data.