# Incompressible limit of the Navier-Stokes model with a growth term

## TL;DR

This paper rigorously derives the incompressible limit of the isentropic compressible Navier-Stokes equations with a growth term, showing convergence to a two-phase free boundary fluid system.

## Contribution

It provides a rigorous mathematical justification for the incompressible limit in the presence of a growth term in the Navier-Stokes equations.

## Key findings

- Incompressible limit leads to a two-phase free boundary fluid system.
- Established convergence from compressible to incompressible models with growth.
- Mathematically justified the limit process for the Navier-Stokes equations with growth term.

## Abstract

Starting from isentropic compressible Navier-Stokes equations with growth term in the continuity equation, we rigorously justify that performing an incompressible limit one arrives to the two-phase free boundary fluid system.