Local well‐posedness and blow‐up criterion for a compressible Navier‐Stokes‐Fourier‐P1 approximate model arising in radiation hydrodynamics

Abstract

We establish a local well-posedness and a blow-up criterion of strong solutions for the compressible Navier-Stokes-Fourier-P1 approximate model arising in radiation hydrodynamics. For the local well-posedness result, we do not need the assumption on the positivity of the initial density and it may vanish in an open subset of the domain.

Uniform regularity for an isentropic compressible MHD-$P1$ approximate model arising in radiation hydrodynamics

“…For example, Fan, Li, Nakamura in [5] (see also [3], [13]) showed non-relativistic and low Mach number limits of the problem. He, Fan, Zhou in [11] (see also [6]) proved the local wellposedness and blow-up criterion of strong solutions. Xie and Klingenberg in [19] studied the non-relativistic limit for the ideal problem (λ = µ = η = 0).…”

Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies

“…The same field of studies comprises the solvability problems in radiation gas‐ and hydrodynamics 65–81 . We also mention works dealing with homogenization of radiative‐conductive heat exchange problems 82–92 and with optimal control in complex heat exchange problems 93–102 .…”