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

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 analyz...

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Bibliographic Details
Published in:Electronic journal of differential equations 2016-09, Vol.2016 (245), p.1-31
Main Authors: Donatella Donatelli, Bernard Ducomet, Marek Kobera, Sarka Necasova
Format: Article
Language:English
Subjects:
classical physics
compressible magnetohydrodynamics
elliptic-parabolic initial boundary value problem
Navier-Stokes-Fourier-Poisson system
plasma
radiation transfer
rotation
stellar radiative zone
vanishing Alfven number
vanishing Mach number
vanishing Peclet number
weak solution
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Summary: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.
ISSN:1072-6691