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

摘要

This paper deals with the spherically symmetric flow of compressible viscousand polytropic ideal fluid in unbounded domain exterior to a ball in$\mathbb{R}^n$ with $n\ge2$. We show that the global solutions are convergentas time goes to infinity. The critical step is obtaining the point-wise boundof the specific volume $v(x,t)$ and the absolute temperature $\theta(x,t)$ fromup and below both for $x$ and $t$. Note that the initial data can bearbitrarily large and, compared with \cite{nn}, our method applies to thespatial dimension $n=2.$ The proof is based on the elementary energy methods.