Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Existence and Lipschitz stability for $\alpha$-dissipative solutions of
  the two-component Hunter-Saxton system
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
3
The categories of this paper are: physics