# Well-posedness of strong solutions to the anelastic equations of stratified viscous flows

## TL;DR

This paper proves the existence and uniqueness of strong solutions to the anelastic equations modeling stratified viscous flows, including cases with vacuum singularities, with solutions existing globally in 2D and locally in 3D.

## Contribution

It establishes well-posedness results for the anelastic equations with physical vacuum singularities, extending previous work to more realistic density profiles.

## Key findings

- Global existence of solutions in 2D for general initial data
- Local (and sometimes global) solutions in 3D for small initial data
- Inclusion of vacuum singularities in the density profile

## Abstract

We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken into account, and the density background profile is permitted to have physical vacuum singularity. The existing time of the solutions is infinite in two dimensions, with general initial data, and in three dimensions with small initial data.