Diffusive limits for a barotropic model of radiative flow

TL;DR

This paper rigorously justifies diffusive limits for a simplified radiative flow model using the P1-approximation, establishing global solutions and convergence in various spatial settings.

Contribution

It provides the first rigorous derivation of diffusive limits for a barotropic radiative flow model with the P1-approximation.

Findings

Existence of global-in-time strong solutions for small data.

Uniform estimates with respect to system coefficients.

Convergence of solutions to limit systems in whole space and periodic domains.

Abstract

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.