Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for the function solution of the homogenuous 2D Boltzmann
  equation with hard potential   We deal with $f\_{t}(dv),$ the solution of the homogeneous $2D$
Boltzmannequation without cutoff. The initial condition $f\_{0}(dv)$ may be
anyprobability distribution (except a Dirac mass). However, for sufficiently
hardpotentials, the semigroup has a regularization property (see
\cite{[BF]}):$f\_{t}(dv)=f\_{t}(v)dv$ for every $t>0.$ The aim of this paper is
to give upperbounds for $f\_{t}(v),$ the most significant one being of type
$f\_{t}(v)\leqCt^{-\eta}e^{-\left\vert v\right\vert ^{\lambda}}$ for some
$\eta,\lambda>0.$

19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph