Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Cauchy problem for the cutoff Boltzmann equation with small
  initial data   We prove the global existence of the non-negative unique mild solution for
the Cauchy problem of the cutoff Boltzmann equation for soft potential model
$-1\leq \gamma< 0$ with the small initial data in three dimensional space. Thus
our result fixes the gap for the case $\gamma=-1$ in three dimensional space in
the authors' previous work where the estimate for the loss term was improperly
used. The other gap there for the case $\gamma=0$ in two dimensional space is
recently fixed by Chen, Denlinger and Pavlovi\'{c}. The initial data $f_{0}$ is
non-negative, small in weighted $L^{3}_{x,v}$ and finite in weighted
$L^{15/8}_{x,v}$. We also show that the solution scatters with respect to the
kinetic transport operator. The novel contribution of this work lies in the
exploration of the symmetric property of the gain term in terms of weighted
estimate. It is the key ingredient for solving the model $-1<\gamma<0$ when
applying the Strichartz estimates.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th