Global weak solutions to the non-relativistic radiation hydrodynamical equations with isothermal fluids

We prove the existence of global entropy solutions in L∞ to the one-dimensional Euler–Boltzmann equations for compressible isothermal fluids and multidimensional Euler–Boltzmann equations for compressible isothermal fluids with spherical symmetry in radiation hydrodynamics. The global weak entropy solutions are constructed using the shock capturing scheme of Godunov type with cut-off technique. The global existence of weak entropy solutions in L∞ with arbitrarily large initial data even containing the vacuum is established with the aid of the compensated compactness method.