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

## TL;DR

This paper derives a 2-D Navier-Stokes-Poisson system with radiation from a 3-D compressible fluid model, demonstrating convergence of weak solutions to strong solutions under certain conditions, advancing understanding of accretion disk dynamics.

## Contribution

It establishes the rigorous derivation and convergence of 3-D compressible radiation fluid solutions to 2-D models relevant for accretion disks, incorporating rotation, gravitation, and radiation effects.

## Key findings

- Weak solutions converge to 2-D strong solutions under small Froude number.
- Convergence holds for all times less than the maximal lifespan of the 2-D solutions.
- The derived models incorporate radiation effects in accretion disk dynamics.

## 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. 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 for all times less than the maximal life time of the strong solution of the 2-D system when the Froude number is small or to the strong solution of the rotating pure 2-D Navier- Stokes system with radiation.