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- W3178202331 abstract "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 mass V(t) satisfies a decay estimate $$V(t)=O(t^{-3/2})$$ (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 form $$C^{-1}t^{-3/2}le |V(t)|$$ for large t ( $$C>1$$ is a constant independent of t). This is achieved by refining the previously obtained pointwise estimates of solutions. We introduce inter-diffusion waves that, 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." @default.
- W3178202331 created "2021-07-19" @default.
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- W3178202331 date "2022-09-05" @default.
- W3178202331 modified "2023-09-23" @default.
- W3178202331 title "Refined Pointwise Estimates for Solutions to the 1D Barotropic Compressible Navier–Stokes Equations: An Application to the Long-Time Behavior of a Point Mass" @default.
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- W3178202331 doi "https://doi.org/10.1007/s00021-022-00732-0" @default.
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