Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Tan $2 \Theta$-Theorem in Fluid Dynamics   We show that the generalized Reynolds number (in fluid dynamics) introduced
by Ladyzhenskaya is closely related to the rotation of the positive spectral
subspace of the Stokes block-operator in the underlying Hilbert space. We also
explicitly evaluate the bottom of the negative spectrum of the Stokes operator
and prove a sharp inequality relating the distance from the bottom of its
spectrum to the origin and the length of the first positive gap.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc