Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global dissipative half-harmonic flows into spheres: small data in
  critical Sobolev spaces   We establish global existence, uniqueness, regularity and long-time
asymptotics of strong solutions to the half-harmonic heat flow and dissipative
Landau-Lifshitz equation, valid for initial data that is small in the
homogeneous Sobolev norm $\dot{H}^{\frac n 2}$ for space dimensions $n \le 3$.

31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga