Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of time averages of weak solutions of the three-dimensional
  Navier-Stokes equations   Using the concept of stationary statistical solution, which generalizes the
notion of invariant measure, it is proved that, in a suitable sense, time
averages of almost every Leray-Hopf weak solution of the three-dimensional
incompressible Navier-Stokes equations converge as the averaging time goes to
infinity. This system of equations is not known to be globally well-posed, and
the above result answers a long-standing problem, extending to this system a
classical result from ergodic theory. It is also showed that, from a
measure-theoretic point of view, the stationary statistical solution obtained
from a generalized limit of time averages is independent of the choice of the
generalized limit. Finally, any Borel subset of the phase space with positive
measure with respect to a stationary statistical solution is such that for
almost all initial conditions in that Borel set and for at least one Leray-Hopf
weak solution starting with that initial condition, the corresponding orbit is
recurrent to that Borel subset and its mean sojourn time within that Borel
subset is strictly positive.

12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg