Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivation of the Boltzmann equation with moderately soft potentials
  from a perturbed Nanbu particles system   We derive the 3D spatially homogeneous Boltzmann's equation with moderately
soft potentials and singular angular interaction, from an interacting particles
system. The collision kernel is of the form $B(z,\sigma)=|z|^{\gamma}b\left(
\frac{z}{|z|}\cdot \sigma\right)$ and for $K>0$,
$\sin(\theta)b\left(\cos(\theta)\right)\sim K\theta^{-1-\nu}$, with $\gamma\in
(-2,-1)$ and $\nu\in(1,2)$ satisfying $\gamma+\nu>0$. We use at the particle
level the regularizing effects of the grazing collisions, in order to control
the singularity of the soft potential. This enables to use a classical
compactness argument, and provide a qualitative convergence result from the
interacting particles system toward the solution of the limit macroscopic
equation.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg