Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow up and global existence for the periodic Phan-Thein-Tanner model   In this paper, we mainly investigate the Cauchy problem for the periodic
Phan-Thein-Tanner (PTT) model. This model is derived from network theory for
the polymeric fluid. We prove that the strong solutions of PTT model will blow
up in finite time if the trace of initial stress tensor $\tr \tau_0(x)$ is
negative. This is a very different with the other viscoelastic model. On the
other hand, we obtain the global existence result with small initial data when
$\tr \tau_0(x)\geq c_0>0$ for some $c_0$. Moreover, we study about the large
time behavior.

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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex