Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow I, II, III
数学专题报告
报告题目(Title)：Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow I, II, III
报告人(Speaker)：徐龙娟（首都师范大学）
地点(Place)：教八楼107
时间(Time)：2023年4月3日(周一), 8:00-11:00
邀请人(Inviter)：李海刚
报告摘要
It is 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. This talk concerns 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 H. Kang in ICM (2022). If time permits, the boundary gradient estimates and the second-order derivatives estimates for Stokes flow when the rigid particles approach the boundary of the matrix will be also discussed.
主讲人简介
徐龙娟，首都师范大学交叉科学研究院特聘副研究员。2019年博士毕业于北京师范大学（导师：李海刚教授），2017年9月至2019年5月在美国布朗大学联合培养（导师：董弘桀教授）。2019年9月至2022年9月先后在韩国延世大学（合作导师：Seick Kim教授）和新加坡国立大学（合作导师：包维柱教授）做博士后研究工作。徐龙娟博士致力于材料科学和流体力学中的偏微分方程理论研究，主要关注材料数学交叉领域的Babuška问题和流体-固体悬浮问题等的应力集中分析和梯度估计，学术论文发表在《Ann. Inst. H. Poincaré Anal. Non Linéaire》、《Calc. Var. Partial Differential Equations》和《SIAM J. Math. Anal.》等国际知名期刊。
