The rotating Navier- Stokes- Fourier- Poisson system on thin domains

TL;DR

This paper proves that weak solutions of the 3D rotating Navier-Stokes-Fourier-Poisson system in thin domains converge to 2D strong solutions as the domain thickness approaches zero, under different Froude number regimes.

Contribution

It establishes the convergence of weak 3D solutions to 2D strong solutions for the rotating Navier-Stokes-Fourier-Poisson system in thin domains, considering different Froude number regimes.

Findings

Weak solutions converge to 2D strong solutions as thickness tends to zero.

Convergence depends on the asymptotic behavior of the Froude number.

Results hold on the time interval where the 2D strong solution exists.

Abstract

We consider the compressible Navier - Stokes - Fourier - Poisson system describing the motion of a viscous heat conducting rotating fluid confined to a straight layer $ \Omega_{\epsilon} = \omega \times (0,\epsilon) $, where $\omega$ is a 2-D domain. The aim of this paper is to show that the weak solutions in the 3D domain converge to the strong solution of the 2-D Navier - Stokes - Fourier - Poisson system $\omega$ as $\epsilon \to 0$ on the time interval, where the strong solution exists. We consider two different regimes in dependence on the asymptotic behaviour of the Froude number.