Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From hard sphere dynamics to the Stokes-Fourier equations: An $L^2$
  analysis of the Boltzmann-Grad limit   We derive the linear acoustic and Stokes-Fourier equations as the limiting
dynamics of a system of N hard spheres of diameter $\epsilon$ in two space
dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N
$\epsilon$ = $\alpha$ $\rightarrow$ $\infty$, using the linearized Boltzmann
equation as an intermediate step. Our proof is based on Lanford's strategy
[18], and on the pruning procedure developed in [5] to improve the convergence
time to all kinetic times with a quantitative control which allows us to reach
also hydrodynamic time scales. The main novelty here is that uniform L 2 a
pri-ori estimates combined with a subtle symmetry argument provide a weak
version of chaos, in the form of a cumulant expansion describing the asymptotic
decorrelation between the particles. A refined geometric analysis of
recollisions is also required in order to discard the possibility of multiple
recollisions.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th