Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Internal exponential stabilization to a non-stationary solution for 3D
  Navier-Stokes equations   We consider the Navier-Stokes system in a bounded domain with a smooth
boundary. Given a sufficiently regular time-dependent global solution, we
construct a finite-dimensional feedback control that is supported by a given
open set and stabilizes the linearized equation. The proof of this fact is
based on a truncated observability inequality, the regularizing property for
the linearized equation, and some standard techniques of the optimal control
theory. We then show that the control constructed for the linear problem
stabilizes locally also the full Navier-Stokes system.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph