Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using periodic boundary conditions to approximate the Navier-Stokes
  equations on $\mathbb{R}^3$ and the transfer of regularity   This paper considers solutions $u_\alpha$ of the three-dimensional
Navier--Stokes equations on the periodic domains $Q_\alpha:=(-\alpha,\alpha)^3$
as the domain size $\alpha\to\infty$, and compares them to solutions of the
same equations on the whole space. For compactly-supported initial data
$u_\alpha^0\in H^1(Q_\alpha)$, an appropriate extension of $u_\alpha$ converges
to a solution $u$ of the equations on ${\mathbb R}^3$, strongly in
$L^r(0,T;H^1({\mathbb R}^3))$, $r\in[1,\infty)$. The same also holds when
$u_\alpha^0$ is the velocity corresponding to a fixed, compactly-supported
vorticity.
  A consequence is that if an initial compactly-supported velocity $u_0\in
H^1({\mathbb R}^3)$ or an initial compactly-supported vorticity $\omega_0\in
H^1({\mathbb R}^3)$ gives rise to a smooth solution on $[0,T^*]$ for the
equations posed on ${\mathbb R}^3$, a smooth solution will also exist on
$[0,T^*]$ for the same initial data for the periodic problem posed on
${Q_\alpha}$ for $\alpha$ sufficiently large; this illustrates a `transfer of
regularity' from the whole space to the periodic case.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int