Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat flow of Yang-Mills-Higgs functionals in dimension two   We consider the heat flow of Yang-Mills-Higgs functional where the base
manifold is a Riemannian surface and the fiber is a compact symplectic
manifold. We show that the corresponding Cauchy problem admits a global weak
solution for any $H^1$-initial data. Moreover, the solution is smooth except
finitely many singularities. We prove an energy identity at finite time
singularities and give a description of the asymptotic behavior at time
infinity.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin