Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity criterion of the 4D Navier-Stokes equations involving two
  velocity field components   We study the Serrin-type regularity criteria for the solutions to the
four-dimensional Navier-Stokes equations and magnetohydrodynamics system. We
show that the sufficient condition for the solution to the four-dimensional
Navier-Stokes equations to preserve its initial regularity for all time may be
reduced from a bound on the four-dimensional velocity vector field to any two
of its four components, from a bound on the gradient of the velocity vector
field to the gradient of any two of its four components, from a gradient of the
pressure scalar field to any two of its partial derivatives. Results are
further generalized to the magnetohydrodynamics system. These results may be
seen as a four-dimensional extension of many analogous results that exist in
the three-dimensional case and also component reduction results of many
classical results.

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The categories of this paper are: stat
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat