Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up results for systems of nonlinear Schr\"odinger equations with
  quadratic interaction   We establish blow-up results for systems of NLS equations with quadratic
interaction in anisotropic spaces. We precisely show finite time blow-up or
grow-up for cylindrical symmetric solutions. With our construction, we moreover
prove some polynomial lower bounds on the kinetic energy of global solutions in
the mass-critical case, which in turn implies grow-up along any diverging time
sequence. Our analysis extends to general NLS systems with quadratic
interactions, and it also provides improvements of known results in the radial
case.

34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph