Large-time behavior for spherically symmetric flow of viscous polytropic gas in exterior unbounded domain with large initial data

Abstract

This paper deals with the spherically symmetric flow of compressible viscous and polytropic ideal fluid in unbounded domain exterior to a ball in ${\mathbb{R}}^n$ with $n\ge 2$. We show that the global solutions are convergent as time goes to infinity. The critical step is obtaining the point-wise bound of the specific volume $v(x,t)$ and the absolute temperature $\theta (x,t)$ from up and below both for $x$ and $t$. Note that the initial data can be arbitrarily large and, compared with \cite{nn}, our method applies to the spatial dimension $n=2.$ The proof is based on the elementary energy methods.

References in corpus (1)

• Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data

Cited by in corpus (2)

• Symmetric flows for compressible heat-conducting fluids with temperature dependent viscosity coefficients
• Global Spherical Symmetric Flows for a Viscous Radiative and Reactive Gas in an Exterior Domain with Large Initial Data