论文标题
Stokes的应力浓度因子流动，两个几乎接触的刚性颗粒
Stress concentration factors for the Stokes flow with two nearly touching rigid particles
论文作者
论文摘要
在本文中，考虑了两个浸入粘性不可压缩的液体中的两个相邻刚性颗粒的数学模型。流量的主要特征是，随着这两个颗粒之间的距离趋于零，由应变张量组成的cauchy应力张量会爆炸。为了清除这种高浓度，统一应力浓度因子的家族在所有维度上都被精确捕获，这决定了Cauchy应力张量是否会爆炸。作为直接应用，我们建立了cauchy应力张量的最佳梯度估计和渐近量，这表明其最大奇异性来自压力。
In this paper, a mathematical model of two adjacent rigid particles immersed into a viscous incompressible fluid is considered. The main feature of the flow is that the Cauchy stress tensor consisting of the strain tensor and the pressure will appear blow-up as the distance between these two particles tends to zero. For the purpose of making clear this high concentration, a family of unified stress concentration factors are precisely captured in all dimensions, which determine whether the Cauchy stress tensor will blow up or not. As a direct application, we establish optimal gradient estimates and asymptotics of the Cauchy stress tensor for Stokes flow, which indicate that its maximal singularity comes from the pressure.
