# Global existence of a radiative Euler system coupled to an electromagnetic field

## TL;DR

This paper proves the global existence and analyzes the long-term behavior of smooth solutions for a coupled radiative Euler and electromagnetic system under small initial data assumptions.

## Contribution

It establishes the first rigorous proof of global smooth solutions for this coupled radiative Euler-electromagnetic system in three dimensions.

## Key findings

- Existence of unique global smooth solutions under small data
- Asymptotic behavior of solutions studied
- Results contribute to understanding radiative hydrodynamics with electromagnetic effects

## 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. Assuming smallness hypotheses for the data, we prove that the problem admits a unique global smooth solution and study its asymptotics.