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 x (0, epsilon), where omega is a 2-D domain. The aim of this paper is to show that the weak solutions in the 3-D domain converge to the strong solution of the 2-D Navier-Stokes-Fourier-Poisson system on omega as epsilon -> 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.

Keywords

• Navier-Stokes-Fourier-Poisson system
• weak solution
• entropy
• rotation
• accretion disk
• thin domains
• dimension reduction
• strong solution