Long-time behavior of several point particles in a 1D viscous compressible fluid
Long-time behavior of several point particles in a 1D viscous compressible fluid
复制标题
一维粘性可压缩流体中多个点粒子的长期行为
DOI：
10.1007/s00028-022-00820-8
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发表时间：
2022
影响因子：
1.4
通讯作者：
Koike Kai
中科院分区：
文献类型：
--
作者：
Osada Hirofumi;Osada Shota;長田翔太;長田翔太;長田翔太;Koike Kai
我们研究了一维粘性可压缩流体中若干点粒子的长期行为。结果表明，点粒子的速度均服从幂律。这一结果扩展了作者以往关于单点粒子长时间行为的研究成果。由于点粒子间波的无限反射，在格林函数的点向估计的推导中出现了新的困难。特别是，在以前的作品中单独使用的微分方程技术是不够的。我们通过仔细分析格林函数在拉普拉斯变量下的结构，特别是它们的渐近性和可解析性，克服了这个问题。
We study the long-time behavior ofseveralpoint particles in a 1D viscous compressible fluid. It is shown that the velocities of the point particles all obey the power law. This result extends author’s previous works on the long-time behavior of asinglepoint particle. New difficulties arise in the derivation of pointwise estimates of Green’s functions due to infinite reflections of waves in-between the point particles. In particular, the differential equation technique used in previous works alone does not suffice. We overcome this by carefully analyzing the structure of Green’s functions in the Laplace variable, especially their asymptotic and analyticity properties.