# Low Mach number limit on thin domains

## TL;DR

This paper proves that solutions of the 3D compressible Navier-Stokes equations in thin domains converge to 2D incompressible flow solutions as the Mach number and domain thickness approach zero, under certain conditions.

## Contribution

It establishes the low Mach number limit for compressible flows in thin domains, connecting 3D compressible and 2D incompressible models.

## Key findings

- Strong convergence of weak solutions to 2D incompressible Navier-Stokes equations
- Validation of the low Mach number limit in thin geometries
- Extension of classical limits to layered domain settings

## Abstract

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to the solution of the 2D incompressible Navier-Stokes equations (Euler equations) when the Mach number $\epsilon $ tends to zero as well as $\delta\rightarrow 0$ (and the viscosity goes to zero).