Global Classical Large Solutions for the Radiation Hydrodynamics Model in Unbounded Domains

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4811-4833, August 2024.
Abstract. This paper is concerned with the global existence of large solutions to the initial and initial boundary value problems for the radiation hydrodynamics model with constant viscosity coefficient and temperature-dependent heat conductivity coefficient. In particular, the initial data and [math] could be arbitrarily large. Compared with the classical compressible Navier–Stokes equations, the research on the radiation hydrodynamics model is more complicated due to the presence of the radiation effect. To overcome difficulties caused by the radiation, inspired by [J. Li and Z. L. Liang, Arch. Ration. Mech. Anal., 220 (2016), pp. 1195–1208; J. H. Zhang and H. J. Zhao, SIAM J. Math. Anal., 55 (2023), pp. 6229–6261], we construct a pointwise estimate between the radiative heat flux and the temperature; then we can establish the desired basic energy estimate by considering that the temperature has lower and upper bounds separately. And once that is obtained, the main result is proved by employing the elementary energy methods.