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 $Ω_ε = ω\times (0,ε)$, where $ω$ 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 $ω$ as $ε\to 0$ on the time interval, where the strong solution exists. We consider two different regimes in dependence on the asymptotic behaviour of the Froude number.

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