Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large, global solutions to the three-dimensional the navier-stokes
  equations without vertical viscosity   The three-dimensional, homogeneous, incompressible Navier-Stokes equations
are studied in the absence of viscosity in one direction. It is shown that
there are arbitrarily large initial data generating a unique global solution,
the main feature of which is that they are slowly varying in the direction
where viscosity is missing. The difficulty arises from the complete absence of
a regularising effect in this direction. The special structure of the nonlinear
term, joint with the divergence-free condition on the velocity field, is
crucial in obtaining the result.

25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th