论文标题
可压缩欧拉方程的时间渐近膨胀与时间依赖性阻尼
The time asymptotic expansion for the compressible Euler equations with time-dependent damping
论文作者
论文摘要
在本文中，我们研究了可压缩的Euler方程，这些方程与时间相关的阻尼$ - \ frac {1} {（1+t）^λ}ρu$。我们提出了围绕广义多孔介质方程（GPME）的自相似解决方案的时间渐近扩展，并严格将这种扩展为$λ\ in（\ frac17,1）$。换句话说，该扩展不是GPME的自相似解，而是通过时间依赖性阻尼对可压缩欧拉方程的解的最佳渐近曲线。
In this paper, we study the compressible Euler equations with time-dependent damping $-\frac{1}{(1+t)^λ}ρu$. We propose a time asymptotic expansion around the self-similar solution of the generalized porous media equation (GPME) and rigorously justify this expansion as $λ\in (\frac17,1)$. In other word, instead of the self-similar solution of GPME, the expansion is the best asymptotic profile of the solution to the compressible Euler equations with time-dependent damping.
