Electron. J. Differential Equations, Vol. 2016 (2016), No. 245, pp. 1-31.

Low Mach and Peclet number limit for a model of stellar tachocline and upper radiative zones

Donatella Donatelli, Bernard Ducomet, Marek Kobera, Sarka Necasova

We study a hydrodynamical model describing the motion of internal stellar layers based on compressible Navier-Stokes-Fourier-Poisson system. We suppose that the medium is electrically charged, we include energy exchanges through radiative transfer and we assume that the system is rotating. We analyze the singular limit of this system when the Mach number, the Alfven number, the Peclet number and the Froude number approache zero in a certain way and prove convergence to a 3D incompressible MHD system with a stationary linear transport equation for transport of radiation intensity. Finally, we show that the energy equation reduces to a steady equation for the temperature corrector.

Submitted June 21, 2016. Published September 10, 2016.
Math Subject Classifications: 35Q35, 76N15, 67W05.
Key Words: Navier-Stokes-Fourier-Poisson system; radiation transfer; compressible magnetohydrodynamics; rotation; stellar radiative zone; weak solution; elliptic-parabolic initial boundary value problem; vanishing Peclet number; vanishing Mach number; vanishing Alfven number; classical physics; plasma.

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Donatella Donatelli
Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica
Universita degli Studi dell'Aquila
67100 L'Aquila, Italy
email: donatella.donatelli@univaq.it
  Bernard Ducomet
F-91297 Arpajon, France
email: bernard.ducomet@cea.fr
Marek Kobera
Mathematical Institute of the Charles University at Prague
Sokolovská 83
186 75 Praha 8, Czech Republic
email: kobera@centrum.cz
  Sárka Necasová
Institute of Mathematics of the Academy of Sciences of the Czech Republic
Zitná 25, 115 67 Praha 1, Czech Republic
email: matus@math.cas.cz

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