Refined Pointwise Estimates for Solutions to the 1D Barotropic Compressible Navier?Stokes Equations: An Application to the Long-Time Behavior of a Point Mass
Refined Pointwise Estimates for Solutions to the 1D Barotropic Compressible Navier?Stokes Equations: An Application to the Long-Time Behavior of a Point Mass
复制标题
一维正压可压缩纳维斯托克斯方程解的精细逐点估计：点质量长期行为的应用
DOI：
10.1007/s00021-022-00732-0
复制
发表时间：
2022
影响因子：
1.3
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;Koike Kai
我们研究了点质量在一维粘性可压缩流体中运动的长期行为。作者先前证明了点质量的速度V(T)满足一个衰减估计(小池在J.Different中)。EQU。271：356-413,2021)。然而，这种衰变估计是否是最佳的还没有完全弄清楚。在这篇文章中，我们通过给出一个简单的充要条件来回答这个问题，这个条件是关于大数的形式的一个下界有效的(是一个常量独立的)。这是通过改进以前获得的解决方案的逐点估计来实现的。我们引入了互扩散波，与经典扩散波一起，给出了点质量周围流体行为的改进近似；这使得对点质量的长期行为有了更深刻的理解。
We study the long-time behavior of a point mass moving in a one-dimensional viscous compressible fluid. The author previously showed that the velocity of the point massV(t) satisfies a decay estimate(Koike in J. Differ. Equ. 271:356–413, 2021). However, whether this decay estimate is optimal or not was not completely understood. In this paper, we answer this question by giving a simple necessary and sufficient condition for the validity of a lower bound of the formfor larget(is a constant independent oft). This is achieved by refining the previously obtained pointwise estimates of solutions. We introduceinter-diffusion wavesthat, together with the classical diffusion waves, give an improved approximation of the fluid behavior around the point mass; this then leads to a sharper understanding of the long-time behavior of the point mass.