Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second derivatives estimate of suitable solutions to the 3D
  Navier-Stokes equations   We study the second spatial derivatives of suitable weak solutions to the
incompressible Navier-Stokes equations in dimension three. We show that it is
locally $L ^{\frac43, q}$ for any $q > \frac43$, which improves from the
current result $L ^{\frac43, \infty}$. Similar improvements in Lorentz space
are also obtained for higher derivatives of the vorticity for smooth solutions.
We use a blow-up technique to obtain nonlinear bounds compatible with the
scaling. The local study works on the vorticity equation and uses De Giorgi
iteration. In this local study, we can obtain any regularity of the vorticity
without any a priori knowledge of the pressure. The local-to-global step uses a
recently constructed maximal function for transport equations.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
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The categories of this paper are: cs
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat