Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the rate of convergence of the two-dimensional $\alpha$-models of
  turbulence to the Navier-Stokes equations   Rates of convergence of solutions of various two-dimensional
$\alpha-$regularization models, subject to periodic boundary conditions, toward
solutions of the exact Navier-Stokes equations are given in the
$L^\infty$-$L^2$ time-space norm, in terms of the regularization parameter $
\alpha$, when $\alpha$ approaches zero. Furthermore, as a paradigm, error
estimates for the Galerkin approximation of the exact two-dimensional
Leray-$\alpha$ model are also presented in the $L^\infty$-$L^2$ time-space
norm. Simply by the triangle inequality, one can reach the error estimates of
the solutions of Galerkin approximation of the $\alpha$-regularization models
toward the exact solutions of the Navier-Stokes equations in the
two-dimensional periodic boundary conditions case.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin