Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak dual pairs and jetlet methods for ideal incompressible fluid models
  in $n\geq 2$ dimensions   We review the role of dual pairs in mechanics and use them to derive
particle-like solutions to regularized incompressible fluid systems. In our
case we have a dual pair resulting from the action of diffeomorphisms on point
particles (essentially by moving the points). We then augment our dual pair by
considering the action of diffeomorphisms on Taylor series, also known as jets.
The augmented weak dual pairs induce a hierarchy of particle-like solutions and
conservation laws with particles carrying a copy of a jet group. We call these
augmented particles jetlets. The jet groups serve as finite-dimensional models
of the diffeomorphism group itself, and so the jetlet particles serve as a
finite-dimensional model of the self-similarity exhibited by ideal
incompressible fluids. The conservation law associated to jetlet solutions is
shown to be a shadow of Kelvin's circulation theorem. Finally, we study the
dynamics of infinite time particle mergers. We prove that two merging particles
at the zeroth level in the hierarchy yield dynamics which asymptotically
approach that of a single particle in the first level in the hierarchy. This
merging behavior is then verified numerically as well as the exchange of
angular momentum which must occur during a near collision of two particles. The
resulting particle-like solutions suggest a new class of meshless methods which
work in dimensions $n \geq 2$ and which exhibit a shadow of Kelvin's
circulation theorem. More broadly, this provides one of the first
finite-dimensional models of self-similarity in ideal fluids.

32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex