Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instantaneous filling of the vacuum for the full Boltzmann equation in
  convex domains   We prove the immediate appearance of a lower bound for mild solutions to the
full Boltzmann equation in the torus or a $C^2$ convex domain with specular
boundary conditions, under the sole assumption of continuity away from the
grazing set of the solution. These results are entirely constructive if the
domain is $C^3$ and strictly convex. We investigate a wide range of collision
kernels, some satisfying Grad's cutoff assumption and others not. We show that
this lower bound is exponential, independent of time and space with explicit
constants depending only on the \textit{a priori} bounds on the solution. In
particular, this lower bound is Maxwellian in the case of cutoff collision
kernels. A thorough study of characteristic trajectories, as well as a
geometric approach of grazing collisions against the boundary are derived.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys