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- W3093307685 abstract "We study the long-time behavior of the system consisting of a one-dimensional barotropic viscous compressible fluid and a freely moving point mass. In our previous paper, we showed that the velocity of the point mass $V(t)$ satisfies an upper bound $|V(t)|leq C(t+1)^{-3/2}$ ($tgeq 0$) for some $C>1$; but we were unable to give a corresponding lower bound. In this paper, by refining the previously obtained pointwise estimates for the fluid variables, we give a necessary and sufficient condition for $V(t)$ to satisfy a lower bound $C^{-1}(t+1)^{-3/2}leq |V(t)|$ ($tgg 1$); when this condition is not met, we obtain a faster decay estimate $|V(t)|leq C(t+1)^{-7/4}$ ($tgeq 0$). This work thus gives a satisfactory answer to the long-time behavior of $V(t)$ (at least for regular and small enough solutions). The main idea of the proof is to refine the leading order terms of the solutions used in the previous paper so that the behavior of the flow around the point mass can be more precisely understood." @default.
- W3093307685 created "2020-10-22" @default.
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- W3093307685 date "2020-10-13" @default.
- W3093307685 modified "2023-09-23" @default.
- W3093307685 title "Refined pointwise estimates for the solutions to the one-dimensional barotropic compressible Navier--Stokes equations: An application to the analysis of the long-time behavior of a moving point mass" @default.
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