Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow
  and local well-posedness in $H^{1}$   In this work, we introduce a novel approach to the problem of gauge choice
for the Yang-Mills equation on the Minkowski space $\mathbb{R}^{1+3}$, which
uses the Yang-Mills heat flow in a crucial way. As this approach does not
possess the drawbacks of the previous approaches, it is expected to be more
robust and easily adaptable to other settings.
  As the first demonstration of the `structure' offered by this new approach,
we will give an alternative proof of the local well-posedness of the Yang-Mills
equations for initial data in $(\dot{H}^{1}_{x} \cap L^{3}_{x}) \times
L^{2}_{x}$, which is a classical result of S. Klainerman and M. Machedon that
had been proved using a different method (local Coulomb gauges). The new proof
does not involve localization in space-time, which had been the key drawback of
the previous method. Based on the results proved in this paper, a new proof of
finite energy global well-posedness of the Yang-Mills equations, also using the
Yang-Mills heat flow, is established in a companion article.

37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph