Low Mach number limit for a model of accretion disk

Donatella Donatelli; Bernard Ducomet; Šárka Nečasová

doi:10.3934/dcds.2018141

Article Contents

2018, Volume 38, Issue 7: 3239-3268. Doi: 10.3934/dcds.2018141

This issue Previous Article Dicritical nilpotent holomorphic foliations Next Article The fractional nonlocal Ornstein-Uhlenbeck equation, Gaussian symmetrization and regularity

Low Mach number limit for a model of accretion disk

1.
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli Studi dell'Aquila, 67100 L'Aquila, Italy
2.
Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, 61 avenue du Général de Gaulle, 94010 Créteil Cedex 10, France
3.
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

Received: April 2017

Revised: January 2018

Published: July 2018

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Abstract

We study an hydrodynamical model describing the motion of thick astrophysical disks relying on compressible Navier-Stokes-Fourier-Poisson system. We also suppose that the medium is electrically charged and we include energy exchanges through radiative transfer. Supposing that the system is rotating, we study the singular limit of the system when the Mach number, the Alfven number and Froude number go to zero and we prove convergence to a 3D incompressible MHD system with radiation with two stationary linear transport equations for transport of radiation intensity.

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Mathematics Subject Classification: Primary: 76N10; Secondary: 76U05.

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