论文标题
对1D压缩可压缩NAVIER的解决方案解决方案的精制估计 - Stokes方程：对点质量的长期行为的应用
Refined pointwise estimates for solutions to the 1D barotropic compressible Navier--Stokes equations: An application to the long-time behavior of a point mass
论文作者
论文摘要
我们研究了一个点质量在一维粘性压缩流体中移动的长期行为。以前，我们证明了点质量$ v（t）$的速度满足衰减估计$ v（t）= o（t^{ - 3/2}）$〜[k。 Koike，J。微分方程\ textbf {271}（2021）356--413]。该结果是作为对压缩纳维尔的自由边界问题的求解估计值的必然估计来获得的。在本文中，我们在衰减估计估计$ v（t）= o（t^{ - 3/2}）$的初始数据上给出了一个简单的必要条件，以使其最佳。这是通过完善先前获得的点估计来实现的：我们利用\ textit {infiffusion waves}，与经典\ textit {扩散波}一起，可以改善点质量周围的流体行为的近似值；然后，这导致对点质量的长时间行为有更详尽的了解。
We study the long-time behavior of a point mass moving in a one-dimensional viscous compressible fluid. Previously, we showed that the velocity of the point mass $V(t)$ satisfies a decay estimate $V(t)=O(t^{-3/2})$~[K. Koike, J. Differential Equations \textbf{271} (2021) 356--413]. This result was obtained as a corollary to pointwise estimates of solutions to a free boundary problem of barotropic compressible Navier--Stokes equations. In this paper, we give a simple necessary and sufficient condition on the initial data for the decay estimate $V(t)=O(t^{-3/2})$ to be optimal. This is achieved by refining the pointwise estimates previously obtained: we make use of \textit{inter-diffusion waves} that, together with the classical \textit{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.
