The rotating Navier- Stokes- Fourier- Poisson system on thin domains
  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. 
Bernard Ducomet, Matteo Caggio, Sarka Necasova, and Milan Pokorny
math.AP