Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon
  equation at energy regularity   This paper is the first part of a trilogy dedicated to a proof of global
well-posedness and scattering of the (4+1)-dimensional mass-less
Maxwell-Klein-Gordon equation (MKG) for any finite energy initial data. The
main result of the present paper is a large energy local well-posedness theorem
for MKG in the global Coulomb gauge, where the lifespan is bounded from below
by the energy concentration scale of the data. Hence the proof of global
well-posedness is reduced to establishing non-concentration of energy. To deal
with non-local features of MKG we develop initial data excision and gluing
techniques at critical regularity, which might be of independent interest.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex