Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 2D Boussinesq equations with logarithmically supercritical
  velocities   This paper investigates the global (in time) regularity of solutions to a
system of equations that generalize the vorticity formulation of the 2D
Boussinesq-Navier-Stokes equations. The velocity $u$ in this system is related
to the vorticity $\omega$ through the relations $u=\nabla^\perp \psi$ and
$\Delta \psi = \Lambda^\sigma (\log(I-\Delta))^\gamma \omega$, which reduces to
the standard velocity-vorticity relation when $\sigma=\gamma=0$. When either
$\sigma>0$ or $\gamma>0$, the velocity $u$ is more singular. The
"quasi-velocity" $v$ determined by $\nabla\times v =\omega$ satisfies an
equation of very special structure. This paper establishes the global
regularity and uniqueness of solutions for the case when $\sigma=0$ and
$\gamma\ge 0$. In addition, the vorticity $\omega$ is shown to be globally
bounded in several functional settings such as $L^2$ for $\sigma>0$ in a
suitable range.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat