Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay of weak solutions and the singular set of the three-dimensional
  Navier-Stokes equations   We consider the behaviour of weak solutions of the unforced three-dimensional
Navier-Stokes equations, under the assumption that the initial condition has
finite energy ($\|u\|^2=\int|u|^2$) but infinite enstrophy ($\|Du\|^2=\int|{\rm
curl} u|^2$). We show that this has to be reflected in the solution for small
times, so that in particular $\|Du(t)\|\to+\infty$ as $t\to0$. We also give
some limitations on this `backwards blowup', and give an elementary proof that
the upper box-counting dimension of the set of singular times can be no larger
than one half. Although similar in flavour, this final result neither implies
nor is implied by Scheffer's result that the 1/2-dimensional Hausdorff measure
of the singular set is zero.

0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th