非线性分析研讨班：Stress analysis and higher derivative estimates for Stokes flow

中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：徐龙娟（首都师范大学）

题  目：Stress analysis and higher derivative estimates for Stokes flow

时  间：2023.09.06（星期三）10:30-11:20

地  点：思源楼S813

摘  要：This talk concerns the estimates for stress concentration between two adjacent rigid inclusions in Stokes flow. We establish the pointwise upper bounds of the gradient and the second-order partial derivatives for Stokes flow in the presence of two closely located strictly convex inclusions in dimensions two and three. Moreover, the lower bounds of the gradient estimates at the narrowest place of the narrow region show the optimality of the blow-up rate. We also show the optimal blow-up rate of Cauchy stress tensor. In dimensions greater than three, the upper bounds of the gradient are established. These results answer the questions raised by Hyeonbae Kang in ICM (2022).