Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full range of blow up exponents for the quintic wave equation in three
  dimensions   For the critical focusing wave equation \Box u = u^5 on R^{3+1} in the radial
case, we prove the existence of type II blow up solutions with scaling
parameter \lambda(t) = t^{-1-\nu} for all \nu >0. This extends the previous
work by the authors and Tataru where the condition \nu> 1/2 had been imposed,
and gives the optimal range of polynomial blow up rates in light of recent work
by Duyckaerts, Kenig and Merle.

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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat