Abstract
We consider a “semi-relativistic” model of radiative viscous compressible Navier–Stokes–Fourier system coupled to the radiative transfer equation extending the classical model introduced in Ducomet et al. (Ann Inst Henri Poincarè AN 28:797–812, 2011) and we study some of its singular limits (low Mach and diffusion) in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field. In the low Mach number case we prove the convergence toward the incompressible Navier–Stokes system coupled to a system of two stationary transport equations. In the diffusion case we prove the convergence toward the compressible Navier–Stokes with modified state functions (equilibrium case) or toward the compressible Navier–Stokes coupled to a diffusion equation (non equilibrium case).
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Communicated by H. Beirão da Veiga
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Ducomet, B., Nečasová, Š. Singular Limits in a Model of Radiative Flow. J. Math. Fluid Mech. 17, 341–380 (2015). https://doi.org/10.1007/s00021-015-0204-y
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DOI: https://doi.org/10.1007/s00021-015-0204-y