题    目：Higher derivative estimates for Lamé system and Stokes equations with closely spaced rigid    inclusions

主讲人：李海刚 教授

单    位：北京师范大学

时    间：2025年11月14日 10:30

地    点：数学院二楼南阶梯教室

摘    要：In this talk we study the interaction between two closely spaced rigid inclusions embedded in an elastic material or suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between them approaches zero. To effectively analyze the singular behavior of solutions, as well as to develop accurate numerical schemes, it is crucial to obtain higher-order derivative estimates---both from an engineering perspective and for the requirements of numerical experiments. We derive high-order derivative estimates for the Lamé system and Stokes equations in the presence of two rigid inclusions. For the Stokes equations, our approach resonates with the method used to handle the incompressibility constraint in the standard convex integration scheme.

简    介：李海刚，北京师范大学教授，博士生导师，教育部青年长江学者。主要从事材料科学中偏微分方程的理论研究，在复合材料中的Babuška问题、亚波长共振、流-固悬浮问题等方面取得系列进展，已在《Adv. Math.》、《Math. Ann.》、《Arch. Ration. Mech. Anal.》、《J. Math. Pures Appl.》、《Trans. AMS》等著名数学刊物发表论文50余篇。荣获教育部霍英东基金，教育部自然科学二等奖，北京市自然科学二等奖等奖励。