Derivation of the Navier-Stokes-Poisson system with radiation for an accretion disk

Abstract

We study the 3-D compressible barotropic radiation fluid dynamics system describing the motion of the compressible rotating viscous fluid with gravitation and radiation confined to a straight layer Ωǫ = ω × (0, ǫ), where ω is a 2-D domain. We show that weak solutions in the 3-D domain converge to the strong solution of — the rotating 2-D Navier–Stokes–Poisson system with radiation in ω as ǫ → 0 for all times less than the maximal life time of the strong solution of the 2-D system when the Froude number is small (Fr = O( √e)), — the rotating pure 2-D Navier–Stokes system with radiation in ω as ǫ → 0 when F r = O(1).