Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-existence of Physical Classical Solutions to Euler's Equations of
  Rigid Body Dynamics   We prove that one cannot construct, for arbitrary initial data,
global-in-time physical classical solutions to Euler's equations of continuum
rigid body mechanics when the constituent rigid bodies are not perfect spheres.
By 'physical' solutions, we mean those that conserve the total linear momentum,
angular momentum and kinetic energy of any given initial datum. The reason for
absence of classical solutions is due to the non-existence of velocity
scattering maps which resolve a collision between two non-spherical rigid
bodies in such a way that (i) they do not interpenetrate, and (ii) total linear
momentum, angular momentum and kinetic energy of the bodies are conserved
through collision. In particular, this implies that when solving Euler's
equations, it is necessary to deal with rigid body trajectories which
experience infinitely-many collisions in a finite time interval.

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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an