Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A priori bound on the velocity in axially symmetric Navier-Stokes
  equations   Let $v$ be the velocity of Leray-Hopf solutions to the axially symmetric
three-dimensional Navier-Stokes equations. Under suitable conditions for
initial values, we prove the following a priori bound \[ |v(x, t)| \le
\frac{C}{r^2} |\ln r|^{1/2}, \]where $r \in (0, 1/2)$ is the distance from $x$
to the z axis, and $C$ is a constant depending only on the initial value.
  This provides a pointwise upper bound (worst case scenario) for possible
singularities while the recent papers \cite{CSTY2} and \cite{KNSS} gave a lower
bound. The gap is polynomial order 1 modulo a half log term.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
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
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs