论文标题
$ l^1 $ - 符合通用的barenblatt解决方案，用于可压缩欧拉方程，并与时间相关阻尼
$L^1$-convergence to generalized Barenblatt solution for compressible Euler equations with time-dependent damping
论文作者
论文摘要
熵解决方案的较大时间行为对可压缩的欧拉尔方程（压力$ p（ρ）=κρ^γ，γ> 1 $），其时间依赖性阻尼（如$ - \ frac {1} {（1+t）^λ} pho）（$ 0}ρu$（$ 0 <λ<1 $）已被调查。通过引入精心设计的迭代方法并使用密集的熵分析，可以证明，可压缩欧拉方程的$ l^\ infty $熵解决方案有限的初始质量在自然$ l^1 $ toutology topology topology topology topology to tocal tocology topology to to poldectional $ l^1 $ topology toplatiental topology（PME）的基本解决方案（pme）具有时间依赖性的差异性差异，由时间依赖性差异固定解决方案。有趣的是，$ l^1 $衰减速率越来越快，因为$λ$增加了$（0，\fracγ{γ+2}] $，而$ [\fracγ{γ+2}，1）$的越来越慢且较慢。
The large time behavior of entropy solution to the compressible Euler equations for polytropic gas (the pressure $p(ρ)=κρ^γ, γ>1$) with time dependent damping like $-\frac{1}{(1+t)^λ}ρu$ ($0<λ<1$) is investigated. By introducing an elaborate iterative method and using the intensive entropy analysis, it is proved that the $L^\infty$ entropy solution of compressible Euler equations with finite initial mass converges strongly in the natural $L^1$ topology to a fundamental solution of porous media equation (PME) with time-dependent diffusion, called by generalized Barenblatt solution. It is interesting that the $L^1$ decay rate is getting faster and faster as $λ$ increases in $(0, \fracγ{γ+2}]$, while is getting slower and slower in $[ \fracγ{γ+2}, 1)$.
