  Here we aim at justifying rigorously different types of physically relevant
diffusive limits for radiative flows. For simplicity, we consider the
barotropic situation, and adopt the so-called P1-approximation of the radiative
transfer equation. In the critical functional framework, we establish the
existence of global-in-time strong solutions corresponding to small enough
data, and exhibit uniform estimates with respect to the coefficients of the
system. Combining with standard compactness arguments, this enables us to
justify rigorously the convergence of the solutions to the expected limit
systems. Our results hold true in the whole space as well as in a periodic box
in dimension n $\ge$ 2.

Analysis of PDEs