Blow up and global existence for the periodic Phan-Thein-Tanner model
Blow up and global existence for the periodic Phan-Thein-Tanner model
复制标题
周期性 Phan-Thein-Tanner 模型的爆炸和全局存在
DOI：
10.1016/j.jde.2019.07.005
复制
发表时间：
2019
影响因子：
2.4
通讯作者：
Yao Zheng an
中科院分区：
文献类型：
--
作者：
Chen Yuhui;Luo Wei;Yao Zheng an
本文主要研究了周期PTT模型的Cauchy问题。该模型是从聚合物流体的网络理论推导出来的。证明了当初应力张量tr τ 0（x）的迹为负时，PTT模型的强解在有限时间内爆破.因此，它与其他粘弹性模型非常不同。另一方面，当tr τ 0（x）≥ c0> 0时，我们在小初值条件下得到了整体解的存在性结果.此外，我们还研究了系统的大时间行为。
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 τ 0 (x) is negative. It is thus very different from the other viscoelastic model. On the other hand, we obtain the global existence result with small initial data when tr τ 0 (x)≥ c 0> 0 for some c 0. Moreover, we study about the large time behavior.