Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two dimensional wave--Klein-Gordon equations with semilinear
  nonlinearities   From the work on the weak-null condition by Lindblad and Rodnianski, it is
well-known that `bad' quadratic sourcing terms are allowed to appear in coupled
semilinear wave equations in three spatial dimensions, provided that such terms
appear as sources for `good' variables and that the good variables feed back
into the system via `good' sourcing terms. Motivated by these ideas, in this
paper we investigate the small data global existence and pointwise decay of
solutions to two systems of coupled wave--Klein-Gordon equations in two spatial
dimensions. In particular, we consider critical semilinear nonlinearities for
the wave equation and below-critical semilinear nonlinearities for the
Klein-Gordon equation. An interesting feature of our two systems is that if the
nonlinearities of our PDEs were to be swapped, the nonlinear term in the wave
equation would lead to finite-time blow-up.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph