Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up of solutions for weakly coupled systems of complex
  Ginzburg-Landau equations   Blow-up phenomena ofvweakly coupled systems of several evolution equations,
especially complex Ginzburg-Landau equationsvis shown by a straightforward ODE
approach not so-called test-function method, which gives the natural blow-up
rate. The difficulty of the proof is that, unlike the single case, terms which
come from the fact that the Laplacian cannot be absorbed into the weakly
coupled nonlinearities. A similar ODE approach is applied to heat systems by
Mochizuki to obtain the lower estimate of lifespan.

12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th