Blow-up criterion for the incompressibleviscoelastic flows
Blow-up criterion for the incompressibleviscoelastic flows
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不可压缩粘弹性流的爆炸准则
DOI：
10.1016/j.jfa.2016.10.024
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发表时间：
2017
影响因子：
1.7
通讯作者：
Zi Ruizhao
中科院分区：
文献类型：
--
作者：
Feng Zefu;Zhu Changjiang;Zi Ruizhao
本文研究了周期域中的不可压粘弹性流动。建立了三维周期初边值问题的Serrin型爆破准则，证明了在速度满足Serrin条件和变形梯度的Lt ∞ LX ∞范数有界的条件下，强解整体存在.对于二维周期初边值问题，我们还建立了基于变形梯度上界的爆破准则。证明的主要成分是一个重要的量的先验估计的假设下，变形梯度是上界的，其散度可以看作是有效的粘性通量。
In this paper, we are concerned with the incompressible viscoelastic flows in the periodic domain. We establish a Serrin-type blow-up criterion for 3-D periodic initial boundary problem, which states a strong solution exists globally, provided that the velocity satisfies Serrin's condition and the L t∞ L x∞-norm of the deformation gradient are bounded. We also establish blow-up criterion in terms of the upper bound of the deformation gradient for 2-D periodic initial boundary problem. The main ingredient of the proof is a priori estimate for an important quantity under the assumption that the deformation gradient is upper bounded, whose divergence can be viewed as the effective viscous flux.