Global existence of a diffusion limit with damping for the compressible radiative Euler system coupled to an electromagnetic field

TL;DR

This paper proves the global existence of smooth solutions for a coupled radiative Euler and electromagnetic system under damping and small data assumptions, advancing understanding of radiative magnetohydrodynamics.

Contribution

It establishes the first global existence result for the 3D radiative compressible Euler system coupled with electromagnetic fields under damping.

Findings

Existence of unique global smooth solutions under damping.

Global solutions hold for small initial data.

The analysis advances the mathematical understanding of radiative MHD systems.

Abstract

We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely the 3D radiative compressible Euler system coupled to an electromagnetic field through the MHD approximation. Assuming the presence of damping together with suitable smallness hypotheses for the data, we prove that this problem admits a unique global smooth solution.