Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Passage from the Boltzmann equation with Diffuse Boundary to the
  Incompressible Euler equation with Heat Convection   We derive the incompressible Euler equations with heat convection with the
no-penetration boundary condition from the Boltzmann equation with the diffuse
boundary in the hydrodynamic limit for the scale of large Reynold number.
Inspired by the recent framework in [30], we consider the Navier-Stokes-Fourier
system with no-slip boundary conditions as an intermediary approximation and
develop a Hilbert-type expansion of the Boltzmann equation around the global
Maxwellian that allows the nontrivial heat transfer by convection in the limit.
To justify our expansion and the limit, a new direct estimate of the heat flux
and its derivatives in the Navier-Stokes-Fourier system is established adopting
a recent Green's function approach in the study of the inviscid limit.

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The categories of this paper are: eess
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat