Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compressible Navier-Stokes approximation for the Boltzmann equation in
  bounded domains   It is well known that the full compressible Navier-Stokes equations can be
deduced via the Chapman-Enskog expansion from the Boltzmann equation as the
first-order correction to the Euler equations with viscosity and
heat-conductivity coefficients of order of the Knudsen number $\epsilon>0$. In
the paper, we carry out the rigorous mathematical analysis of the compressible
Navier-Stokes approximation for the Boltzmann equation regarding the
initial-boundary value problems in general bounded domains. The main goal is to
measure the uniform-in-time deviation of the Boltzmann solution with diffusive
reflection boundary condition from a local Maxwellian with its fluid quantities
given by the solutions to the corresponding compressible Navier-Stokes
equations with consistent non-slip boundary conditions whenever $\epsilon>0$ is
small enough. Specifically, it is shown that for well chosen initial data
around constant equilibrium states, the deviation weighted by a velocity
function is $O(\epsilon^{1/2})$ in $L^\infty_{x,v}$ and $O(\epsilon^{3/2})$ in
$L^2_{x,v}$ globally in time. The proof is based on the uniform estimates for
the remainder in different functional spaces without any spatial regularity.
One key step is to obtain the global-in-time existence as well as
uniform-in-$\epsilon$ estimates for regular solutions to the full compressible
Navier-Stokes equations in bounded domains when the parameter $\epsilon>0$ is
involved in the analysis.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th