论文标题
通过阻尼通过Orlicz空间技术进行压缩的Euler方程的寿命估算
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
论文作者
论文摘要
在本文中，我们对可压缩欧拉系统的寿命估计值感兴趣，并具有依赖性阻尼和小的初始扰动。我们采用了非线性波方程爆破研究中的一些技术。新颖性在于引入工具从Orlicz空间理论引入工具，以处理从压力$ p \ equiv p（ρ）$中出现的非线性术语，该术语接受了$ρ-1$的大小值，它是$ρ-1$的不同渐近行为，为$ρ$。因此，我们可以在\ {2,3 \} $中建立$ n \ in \ {2,3 \} $，仅取决于尺寸$ n $和阻尼强度，并且独立于绝热索引$γ> 1 $。我们猜测结果是最佳的。此处采用的方法不仅改善了\ {2,3 \} $的$ n \ $ n \的寿命上限，而且在研究相关问题的研究中具有潜在的应用。
In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blow-up study of nonlinear wave equations. The novelty consists in the introduction of tools from the Orlicz spaces theory to handle the nonlinear term emerging from the pressure $p \equiv p(ρ)$, which admits different asymptotic behavior for large and small values of $ρ-1$, being $ρ$ the density. Hence we can establish, in high dimensions $n\in\{2,3\}$, unified upper bounds of the lifespan estimate depending only on the dimension $n$ and on the damping strength, and independent of the adiabatic index $γ>1$. We conjecture our results to be optimal. The method employed here not only improves the known upper bounds of the lifespan for $n\in\{2,3\}$, but has potential application in the study of related problems.
