Global Spherical Symmetric Flows for a Viscous Radiative and Reactive Gas in an Exterior Domain with Large Initial Data

TL;DR

This paper establishes the global existence, uniqueness, and long-term behavior of spherically symmetric solutions for a viscous radiative and reactive gas in an exterior domain, emphasizing uniform bounds on key physical quantities.

Contribution

It provides new uniform estimates and proves global well-posedness for large initial data in an unbounded exterior domain.

Findings

Proved global existence and uniqueness of solutions.

Established uniform bounds on specific volume and temperature.

Analyzed large-time asymptotic behavior of solutions.

Abstract

In this paper, we study the global existence, uniqueness and large-time behavior of spherically symmetric solution of a viscous radiative and reactive gas in an unbounded domain exterior to the unit sphere in $\mathbb{R}^{n}$ for $n\geq 2$. The key point in the analysis is to deduce certain uniform estimates on the solutions, especially on the uniform positive lower and upper bounds on the specific volume and the temperature.