Nonequilibrium–diffusion limit of the compressible Euler radiation model in ℝ3

This article studies the nonequilibrium–diffusion limit of the compressible Euler model arising in radiation hydrodynamics in $$$ {\mathrm{\mathbb{R}}}^3 $$$ with the general initial data. Combining the moment method with Hilbert expansion, we show that the radiative intensity can be approximated by the sum of interior solution and initial layer. We also show that the solution satisfied by the density, temperature, and velocity can be approximated by the interior solutions. Our results can be considered as an extension from ${\mathrm{𝕋}}^3$ in arXiv.2312.15208 by Ju, Li, and Zhang to $$$ {\mathrm{\mathbb{R}}}^3 $$$. In contrast to arXiv.2312.15208, we get the exact convergence rates by studying the error system derived from the primitive system, the zeroth-order to the second-order about the radiative intensity, and the zeroth-order about the hydrodynamics.