On the equations of thermally radiative magnetohydrodynamics

An initial–boundary value problem is considered for the viscous compressible thermally radiative magnetohydrodynamic (MHD) flows coupled to self-gravitation describing the dynamics of gaseous stars in a bounded domain of R3R3. The conservative boundary conditions are prescribed. Compared to Ducomet–Feireisl [13] (also see, for instance, Feireisl [18], Feireisl–Novotný [20]), a rather more general constitutive relationship is given in this paper. The analysis allows for the initial density with vacuum. Every transport coefficient admits a certain temperature scaling. The global existence of a variational (weak) solution with any finite energy and finite entropy data is established through a three-level approximation and methods of weak convergence.