Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smoothing for the Zakharov & Klein-Gordon-Schr\"{o}dinger Systems on
  Euclidean Spaces   This paper studies the regularity of solutions to the Zakharov and
Klein-Gordon-Schr\"{o}dinger systems at low regularity levels. The main result
is that the nonlinear part of the solution flow falls in a smoother space than
the initial data. This relies on a new bilinear $X^{s,b}$ estimate, which is
proved using delicate dyadic and angular decompositions of the frequency
domain. Such smoothing estimates have a number of implications for the
long-term dynamics of the system. In this work, we give a simplified proof of
the existence of global attractors for the Klein-Gordon-Schr\"{o}dinger flow in
the energy space for dimensions $d = 2,3$. Secondly, we use smoothing in
conjunction with a high-low decomposition to show global well-posedness of the
Klein-Gordon-Schr\"{o}dinger evolution on $\mathbb{R}^4$ below the energy space
for sufficiently small initial data.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org