Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fluid dynamic limit of Boltzmann equation for granular hard--spheres in
  a nearly elastic regime   In this paper, we provide the first rigorous derivation of hydrodynamic
equations from the Boltzmann equation for inelastic hard spheres with small
inelasticity. The hydrodynamic system that we obtain is an incompressible
Navier-Stokes-Fourier system with self-consistent forcing terms and is thus the
first hydrodynamic system that properly describes rapid granular flows. To do
that, we write our Boltzmann equation in nondimensional form introducing the
dimensionless Knudsen number which is intended to tend to 0. The difficulties
are then manyfold, the first one coming from the fact that the original
Boltzmann equation is free-cooling and thus requires a self-similar change of
variables to work with an equation that has an homogeneous steady state. The
latter is not explicit and is heavy-tailed, which is a major obstacle to adapt
energy estimates and spectral analysis. One of the main challenges here is to
understand the relation between the restitution coefficient (which quantifies
the loss of energy at the microscopic level) and the Knudsen number. This is
done identifying the correct nearly elastic regime to capture nontrivial
hydrodynamic behavior. We are then able to prove exponential stability
uniformly with respect to the Knudsen number of the solution of our rescaled
Boltzmann equation in a close to equilibrium regime. Finally, we prove that our
solution to the Boltzmann equation converges in some very specific weak sense
towards some hydrodynamic solution which depends on time and space variables
only through macroscopic quantities. Such macroscopic quantities are solutions
to a suitable modification of the incompressible Navier-Stokes-Fourier system
which appears to be new in this context.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
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The categories of this paper are: econ
16
The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: nlin