Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instantaneous smoothing and exponential decay of solutions for a
  degenerate evolution equation with application to Boltzmann's equation   We establish an instantaneous smoothing property for decaying solutions on
the half-line $(0,+\infty)$ of certain degenerate Hilbert space-valued
evolution equations arising in kinetic theory, including in particular the
steady Boltzmann equation. Our results answer the two main open problems posed
by Pogan and Zumbrun in their treatment of $H^1$ stable manifolds of such
equations, showing that $L^2_{loc}$ solutions that remain sufficiently small in
$L^\infty$ (i) decay exponentially, and (ii) are $C^\infty$ for $t>0$, hence
lie eventually in the $H^1$ stable manifold constructed by Pogan and Zumbrun

27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph