Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-Time Behavior of a Point Mass in a One-Dimensional Viscous
  Compressible Fluid and Pointwise Estimates of Solutions   We consider the motion of a point mass in a one-dimensional viscous
compressible barotropic fluid. The fluid--point mass system is governed by the
barotropic compressible Navier--Stokes equations and Newton's equation of
motion. Our main result concerns the long-time behavior of the fluid and the
point mass, and it gives pointwise convergence estimates of the volume ratio
and the velocity of the fluid to their equilibrium values. As a corollary, it
is shown that the velocity $V(t)$ of the point mass satisfies a decay estimate
$|V(t)|=O(t^{-3/2})$ --- a faster decay compared to $t^{-1/2}$ known for the
motion of a point mass in the viscous Burgers fluid~[J.~L.~V{\'{a}}zquez and
E.~Zuazua, Comm. Partial Differential Equations \textbf{28} (2003),
1705--1738]. The rate $-3/2$ is essentially related to the compressibility and
the nonlinearity. As a consequence, it follows that the point mass is convected
only a finite distance as opposed to the viscous Burgers case. The main tool
used in the proof is the pointwise estimates of Green's function. It turns out
that the understanding of the time-decay properties of the transmitted and
reflected waves at the point mass is essential for the proof.

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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph