Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The stability of Sobolev norms for the linear wave equation with
  unbounded perturbations   In this paper, we prove that the Sobolev norm of solutions of the linear wave
equation with unbounded perturbations of order one stay bounded for the all
time. The main proof is based on the KAM reducibility of the linear wave
equation. To the best of our knowledge, this is the first reducibility result
of the linear wave equation with general quasi-periodic unbounded potentials on
the torus.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga