Diffusion asymptotics of a coupled model for radiative transfer: general initial data (Q6542407)

The authors consider a Cauchy problem in \(\mathbb{R}^3\) (unit sphere) with general initial data for a coupled model that consists of Euler system and a radiative transfer equation. The model contains a small parameter. The aim of the paper is find the nonequilibrim asymptotic regime for the system. Under the assumption of sufficient smoothness of the initial data (in terms of \(L^\infty\), Sobolev spaces, and \(C^6\) for the velocity field), local existence (on a segment independent of the small parameter) and uniqueness are proved together with regularity estimates. The asymptotic behavior for the vanishing small parameter is described in terms of zero-limit in the Sobolev sense.