Blow-up criterion for an incompressible Navier-Stokes/Allen-Cahn system with different densities
Blow-up criterion for an incompressible Navier-Stokes/Allen-Cahn system with different densities
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DOI：
10.3934/dcdsb.2016009
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发表时间：
2016-04
影响因子：
1.2
通讯作者：
Yinghua Li;S. Ding;Mingxia Huang
中科院分区：
文献类型：
--
作者：
Yinghua Li;S. Ding;Mingxia Huang
本文研究了在有界区域$\Omega\subset\mathbb R^N$（$N= 2，3 $）中描述不同密度粘性不可压缩流体两相流扩散界面模型的耦合Navier-Stokes/Allen-Cahn方程组。我们建立了一个判据，在有限时间的速度梯度的变形张量的最大模和相场变量的梯度的最大模的平方在二维时间积分的时间，这种解决方案的可能打破。在3D中，还需要速度的最大范数的平方的时间积分。这里，我们假设初始密度函数有一个正的下界。
This paper is concerned with a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain $\Omega\subset\mathbb R^N$($N=2,3$). We establish a criterion for possible break down of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of phase field variable in 2D. In 3D, the temporal integral of the square of maximum norm of velocity is also needed. Here, we suppose the initial density function $\rho_0$ has a positive lower bound.