Global Smooth Radially Symmetric Solutions to a Multidimensional Radiation Hydrodynamics Model

TL;DR

This paper proves the existence of unique, globally smooth, radially symmetric solutions to a three-dimensional radiative Euler equation with small initial data, demonstrating a dissipative effect of radiation in multidimensional flows.

Contribution

It establishes the first rigorous result for global regularity of multidimensional radiative Euler equations with small initial data.

Findings

Existence of global smooth solutions in 3D bounded domains.

Radial symmetry plays a key role in the analysis.

Radiation effects induce dissipation, preventing singularities.

Abstract

The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although solutions of the compressible Euler system will generally develop singularity no matter how smooth and small the initial data are, it is believed that the radiation effect does imply some dissipative mechanism, which can guarantee the global regularity of the solutions of the radiative Euler equations at least for small initial data. Such an expectation was rigorously justified for the one-dimensional case, as for the multidimensional case, to the best of our knowledge, no result was available up to now. The main purpose of this paper is to show that the initial-boundary value problem of such a radiative Euler equation in a three-dimensional bounded concentric annular domain does admit a unique global smooth radially symmetric solution provided that the initial data is sufficiently small.