标题： 三维斯托克斯流中悬浮刚性粒子接近边界时的应力爆破分析 显示英文标题

标题： Stress blow-up analysis when suspending rigid particles approach boundary in 3D Stokes flow

摘要： 应力集中是在流体-固体模型研究中常见的现象。 在本文中，我们研究了当刚性颗粒接近三维基体边界时斯托克斯流的边界梯度估计和二阶导数估计。 我们对来自预定各种边界数据的应力爆破率的影响进行了分类：局部常数情况和局部多项式情况。 我们的结果适用于一般的凸包，包括实际中两个重要的情况，球形包和椭球形包。 在狭窄区域中也获得了柯西应力的爆破率。 我们在大于三的高维空间中建立了相应的估计。 显示英文摘要

摘要： The stress concentration is a common phenomenon in the study of fluid-solid model. In this paper, we investigate the boundary gradient estimates and the second order derivatives estimates for the Stokes flow when the rigid particles approach the boundary of the matrix in dimension three. We classify the effect on the blow-up rates of the stress from the prescribed various boundary data: locally constant case and locally polynomial case. Our results hold for general convex inclusions, including two important cases in practice, spherical inclusions and ellipsoidal inclusions. The blow-up rates of the Cauchy stress in the narrow region are also obtained. We establish the corresponding estimates in higher dimensions greater than three.