Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of several rigid bodies in a two-dimensional ideal fluid and
  convergence to vortex systems   We consider the motion of several solids in a bounded cavity filled with a
perfect incompressible fluid, in two dimensions. The solids move according to
Newton's law, under the influence of the fluid's pressure, and the fluid
dynamics is driven by the 2D incompressible Euler equations, which are set on
the time-dependent domain corresponding to the cavity deprived of the sets
occupied by the solids. We assume that the fluid vorticity is initially bounded
and that the circulations around the solids may be non-zero. The existence of a
unique corresponding solution, \`a la Yudovich, to this system, up to a
possible collision, is known. In this paper we identify the limit dynamics of
the system when the radius of some of the solids converge to zero depending on
how, for each body, the inertia is scaled with the radius. We obtain in the
limit some point vortex systems for the solids converging to particles and a
form of Newton's law for the solids that have a fixed radius; for the fluid we
obtain an Euler-type system. This extends earlier works to the case of several
moving rigid bodies. A crucial point is to understand the interaction, through
the fluid, between small moving solids, and for that we use some normal forms
of the ODEs driving the motion of the solids in two steps: first we use a
normal form for the system coupling the time-evolution of all the solids to
obtain a rough estimate of the acceleration of the bodies, then we turn to some
normal forms that are specific to each small solid, with an appropriate
modulation related to the influence of the other solids and of the fluid
vorticity, to obtain some precise uniform a priori estimates of the velocities
of the bodies, and then pass to the limit.

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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con