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

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.