# Derivation of the Navier–Stokes–Poisson System with Radiation for an Accretion Disk

Derivation of the Navier–Stokes–Poisson System with Radiation for an Accretion Disk 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 $$\Omega _{\epsilon } = \omega \times (0,\epsilon )$$ Ω ϵ = ω × ( 0 , ϵ ) , where $$\omega$$ 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 $$\omega$$ ω as $$\epsilon \rightarrow 0$$ ϵ → 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 $$(Fr={\mathcal {O}}(\sqrt{\epsilon }))$$ ( F r = O ( ϵ ) ) ,—the rotating pure 2-D Navier–Stokes system with radiation in $$\omega$$ ω as $$\epsilon \rightarrow 0$$ ϵ → 0 when $$Fr={\mathcal {O}}(1)$$ F r = O ( 1 ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

# Derivation of the Navier–Stokes–Poisson System with Radiation for an Accretion Disk

, Volume 20 (2) – Jan 9, 2018
23 pages

Publisher
Springer International Publishing
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0358-x
Publisher site
See Article on Publisher Site

### 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 $$\Omega _{\epsilon } = \omega \times (0,\epsilon )$$ Ω ϵ = ω × ( 0 , ϵ ) , where $$\omega$$ 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 $$\omega$$ ω as $$\epsilon \rightarrow 0$$ ϵ → 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 $$(Fr={\mathcal {O}}(\sqrt{\epsilon }))$$ ( F r = O ( ϵ ) ) ,—the rotating pure 2-D Navier–Stokes system with radiation in $$\omega$$ ω as $$\epsilon \rightarrow 0$$ ϵ → 0 when $$Fr={\mathcal {O}}(1)$$ F r = O ( 1 ) .

### Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Jan 9, 2018

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