论文标题
二维Stokes流动中两个相邻刚性夹杂物之间应力浓度的估计值
Estimates for stress concentration between two adjacent rigid inclusions in two-dimensional Stokes flow
论文作者
论文摘要
在材料科学和流体力学中，重要的是研究两个夹杂物之间狭窄区域的田间增强。包括颗粒悬浮液在内的复杂流体通常会导致复杂的流动行为。在本文中，当两个刚性颗粒紧密间隔悬浮在一个开放的界面域，并在尺寸二维中远离边界时，我们建立了梯度的上限和Stokes流量的二阶部分衍生物。此外，颈部区域最狭窄位置的梯度估计值的下限显示了爆炸速率的最佳性。这些结果对于具有任意形状的夹杂物有效。
It is vital important in material sciences and fluid mechanics to study the field enhancements in the narrow region between two inclusions. Complex fluids including particle suspensions usually result in complicated flow behavior. In this paper we establish the pointwise upper bounds of the gradient and the second-order partial derivatives for the Stokes flow when two rigid particles are closely spaced suspending in an open bounded domain and away from the boundary in dimension two. Moreover, the lower bounds of the gradient estimates at the narrowest place of the neck region show the optimality of the blow-up rate. These results are valid for inclusions with arbitrary shape.
