Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Large-Time Behavior of the Vlasov-Maxwell-Boltzmann System in
  the Whole Space   In this paper we study the large-time behavior of classical solutions to the
two-species Vlasov-Maxwell-Boltzmann system in the whole space $\R^3$. The
existence of global in time nearby Maxwellian solutions is known from [34] in
2006. However the asymptotic behavior of these solutions has been a challenging
open problem. Building on our previous work [10] on time decay for the simpler
Vlasov-Poisson-Boltzmann system, we prove that these solutions converge to the
global Maxwellian with the optimal decay rate of $O(t^{-3/2+\frac{3}{2r}})$ in
$L^2_\xi(L^r_x)$-norm for any $2\leq r\leq \infty$ if initial perturbation is
smooth enough and decays in space-velocity fast enough at infinity. Moreover,
some explicit rates for the electromagnetic field tending to zero are also
provided.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph