Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of Acoustic Wave Propagation in a Thin Moving Fluid   We study the propagation of acoustic waves in a fluid that is contained in a
thin two-dimensional tube, and that it is moving with a velocity profile that
only depends on the transversal coordinate of the tube. The governing equations
are the Galbrun equations, or, equivalently, the linearized Euler equations. We
analyze the approximate model that was recently derived by Bonnet-Bendhia,
Durufl\'e and Joly to describe the propagation of the acoustic waves in the
limit when the width of the tube goes to zero. We study this model for strictly
monotonic stable velocity profiles. We prove that the equations of the model of
Bonnet-Bendhia, Durufl\'e and Joly are well posed, i.e., that there is a unique
global solution, and that the solution depends continuously on the initial
data. Moreover, we prove that for smooth profiles the solution grows at most as
$t^3$ as $t \to \infty$, and that for piecewise linear profiles it grows at
most as $t^4$. This establishes the stability of the model in a weak sense.
These results are obtained constructing a quasi-explicit representation of the
solution. Our quasi-explicit representation gives a physical interpretation of
the propagation of acoustic waves in the fluid and it provides an efficient way
to compute numerically the solution.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph