Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tamed 3D Navier-Stokes Equation: Existence, Uniqueness and Regularity   In this paper, we prove the existence and uniqueness of a smooth solution to
a tamed 3D Navier-Stokes equation in the whole space. In particular, if there
exists a bounded smooth solution to the classical 3D Navier-Stokes equation,
then this solution satisfies our tamed equation. Moreover, using this
renormalized equation we can give a new construction for a suitable weak
solution of the classical 3D Navier-Stokes equation introduced in [Scheffer:
Hausdorff measure and the Navier-Stokes equations. Comm. Math. Phys., 1977] and
[Caffarelli, Kohn, Nirenberg: Partial regularity of suitable weak solutions of
the Navier-Stokes equations. Comm. Pure Appl. Math., 1982].

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph