One-dimensional maximum entropy radiation hydrodynamics: three-moment theory

We analyse in detail the three-moment maximum entropy radiation hydrodynamics which describes the motion of a gas of massless particles obeying Maxwell-Boltzmann, Bose-Einstein or Fermi-Dirac statistics. The primitive fields of this hydrodynamics are the energy density, the heat flux and the flux of the heat flux. We focus on the study of one-dimensional flows. Thus, the independent or non-vanishing variables defining the state of the gas are 3 in number. Two formulations are used: the formulation in terms of the Lagrange multipliers of the constrained optimization problem and the formulation in terms of the primitive fields. We prove that there exists a diffeomorphism between the open convex domain of Lagrange multipliers and the whole natural domain of primitive fields.