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

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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 \( \Omega _{\epsilon } = \omega \times (0,\epsilon ) \), where \( \omega \) 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 \(\omega \) as \(\epsilon \rightarrow 0\) for all times less than the maximal life time of the strong solution of the 2-D system when the Froude number is small \((Fr={\mathcal {O}}(\sqrt{\epsilon }))\),—the rotating pure 2-D Navier–Stokes system with radiation in \(\omega \) as \(\epsilon \rightarrow 0\) when \(Fr={\mathcal {O}}(1)\).

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Acknowledgements

B. D. is partially supported by the ANR project INFAMIE (ANR-15-CE40-0011) Š. N. is supported by the Czech Science Foundation, grant No. 201-16-03230S and by RVO 67985840. Part of this paper was written during her stay in CEA and she would like to thank Prof. Ducomet for his hospitality during her stay. M. P. was supported by the Czech Science Foundation, Grant No. 201-16-03230S. M.A.R.B. was partially supported by MINECO grant MTM2015-69875-P (Ministerio de Economía y Competitividad, Spain) with the participation of FEDER. She would also like to thank Prof. Nečasová for her hospitality during the stay in Prague. Last, but not least, we would like to thank an anonymous referee for careful reading of the original manuscript and for his suggestions which helped to improve the quality of the paper.

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Authors and Affiliations

  1. Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, 61 avenue du Général de Gaulle, 94010, Créteil Cedex 10, France

    Bernard Ducomet

  2. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic

    Šárka Nečasová

  3. Mathematical Institute of Charles University, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Milan Pokorný

  4. Dpto. Ecuaciones Diferenciales y Análisis Numérico and IMUS, Facultad de Matemáticas, Universidad de Sevilla, C/Tarfia, s/n, 41012, Sevilla, Spain

    M. Angeles Rodríguez–Bellido

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  1. Bernard Ducomet
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  2. Šárka Nečasová
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  4. M. Angeles Rodríguez–Bellido
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Correspondence to Šárka Nečasová.

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Communicated by H. Beirao da Veiga.

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Ducomet, B., Nečasová, Š., Pokorný, M. et al. Derivation of the Navier–Stokes–Poisson System with Radiation for an Accretion Disk. J. Math. Fluid Mech. 20, 697–719 (2018). https://doi.org/10.1007/s00021-017-0358-x

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