论文标题
带压缩的可压缩欧拉方程的时间渐近扩展
The time asymptotic expansion for the compressible Euler equations with damping
论文作者
论文摘要
在1992年，Hsiao和Liu \ cite {hsiao-liu-1}首先表明，具有阻尼时间 - 杂种的可压缩欧拉方程的解决方案会收敛到扩散波$（\ bar v，\ bar v，\ bar u）的多孔介质方程。在\ cite {geng-huang-jin-wu}中，我们提出了围绕扩散波$ $（\ bar v，\ bar u）$的时间 - 肿瘤扩展，这是比$（\ bar v v，\ bar u）$更好的渐近配置文件。在本文中，我们严格地通过近似绿色功能方法和能量估计来证明时间复杂的扩展合理。此外，解决阻尼的可压缩欧拉方程的较大时间行为准确地以渐近膨胀为特征。
In 1992, Hsiao and Liu \cite{Hsiao-Liu-1} firstly showed that the solution to the compressible Euler equations with damping time-asymptotically converges to the diffusion wave $(\bar v, \bar u)$ of the porous media equation. In \cite{Geng-Huang-Jin-Wu}, we proposed a time-asymptotic expansion around the diffusion wave $(\bar v, \bar u)$, which is a better asymptotic profile than $(\bar v, \bar u)$. In this paper, we rigorously justify the time-asymptotic expansion by the approximate Green function method and the energy estimates. Moreover, the large time behavior of the solution to compressible Euler equations with damping is accurately characterized by the time asymptotic expansion.
