Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay of the Boltzmann equation with the specular boundary condition in
  non-convex cylindrical domains   A basic question about the existence and stability of the Boltzmann equation
in general non-convex domain with the specular reflection boundary condition
has been widely open. In this paper, we consider cylindrical domains whose
cross sections are general non-convex analytic planar domain. We establish the
global-wellposedness and asymptotic stability of the Boltzmann equation with
the specular reflection boundary condition in such domains. Our method consists
of sharp classification of billiard trajectories which bounce infinitely many
times or hit the boundary tangentially at some moment, and a delicate
construction of an $\e$-tubular neighborhood of such trajectories. Analyticity
of the boundary is crucially used. Away from such $\e$-tubular neighborhood, we
control the number of bounces of trajectories and its' distance from singular
sets in a uniform fashion. The worst case, sticky grazing set, can be excluded
by cutting off small portion of the temporal integration. Finally we apply a
method of \cite{KimLee} by the authors and achieve a pointwise estimate of the
Boltzmann solutions.

34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex