Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The multilayer shallow water system in the limit of small density
  contrast   We study the inviscid multilayer Saint-Venant (or shallow-water) system in
the limit of small density contrast. We show that, under reasonable
hyperbolicity conditions on the flow and a smallness assumption on the initial
surface deformation, the system is well-posed on a large time interval, despite
the singular limit. By studying the asymptotic limit, we provide a rigorous
justification of the widely used rigid-lid and Boussinesq approximations for
multilayered shallow water flows. The asymptotic behaviour is similar to that
of the incompressible limit for Euler equations, in the sense that there exists
a small initial layer in time for ill-prepared initial data, accounting for
rapidly propagating "acoustic" waves (here, the so-called barotropic mode)
which interact only weakly with the "incompressible" component (here,
baroclinic).

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The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol