Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a critical Leray$-\alpha$ model of turbulence   This paper aims to study a family of Leray-$\alpha$ models with periodic
bounbary conditions. These models are good approximations for the Navier-Stokes
equations. We focus our attention on the critical value of regularization
"$\theta$" that garantees the global well-posedness for these models. We
conjecture that $\theta= 1/4$ is the critical value to obtain such results.
  When alpha goes to zero, we prove that the Leray-$\alpha$ solution, with
critical regularization, gives rise to a suitable solution to the Navier-Stokes
equations. We also introduce an interpolating deconvolution operator that
depends on "$\theta$". Then we extend our results of existence, uniqueness and
convergence to a family of regularized magnetohydrodynamics equations.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat