Nonrelativistic Limit of the Compressible Navier--Stokes--Fourier--P1 Approximation Model Arising in Radiation Hydrodynamics

Abstract

Abstract. As is well-known that the general radiation hydrodynamics models include two mainly coupled parts: one is macroscopic fluid part, which is governed by the compressible Navier-Stokes-Fourier equations; another is radiation field part, which is described by the transport equation of photons. Under the two physical approximations: "gray" approximation and P1 approximation, one can derive the so-called Navier-Stokes-Fourier-P1 approximation radiation hydrodynamics model from the general one. In this paper we study the non-relativistic limit problem for the Navier-Stokes-Fourier-P1 approximation model due to the fact that the speed of light is much larger than the speed of the macroscopic fluid. Our results give a rigorous derivation of the widely used macroscopic model in radiation hydrodynamics.

A limit problem for three-dimensional ideal compressible radiation magneto-hydrodynamics

“…It is noted that the damping terms in equations (2.5)-(2.6) also play a crucial role in controlling the nonlinear coupled terms, which are socalled "good" properties from radiation fields. However, compared with the limit problem considered in [5], there is no any diffusion effect in the systems (1.32)-(1.39) and (1.40)-(1.45). Consequently, the symmetrizers of the systems (1.32)-(1.39) and (1.40)-(1.45) are essentially used to overcome the difficulties caused by the flux terms.…”

“…Besides the singularity in (1.36)-(1.37), there exists an extra singularity caused by the coupling of I 0 and I 1 in the momentum and temperature equations. In this paper, we shall overcome all these difficulties by adopting and modifying the elaborate nonlinear energy method developed in [3][4][5]. First, we derive the error system (2.1)-(2.6) by utilizing the original system (1.32)-(1.37) and the limit system (1.40)-(1.44).…”

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

“…Based on the above local existence result, we (see also Danchin and Ducomet and Jiang et al) established the non‐relativistic and low Mach number limits of the problems .…”

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

“…Based on the above local existence result, we [] (see also []) establish non‐relativistic and low Mach number limits of the problem –.…”