Academic Report of School of Mathematical Sciences [2026] No. 009

(Series Report for High-Level University Construction No. 1268)

Title：Babu\v{s}ka Problem in Composite Material and its Applications

Speaker：Professor Haigang Li (Beijing Normal University)

Time：14:00-15:00, Jan. 19, 2026

Location：Huiwen Building 1420

Abstract：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 optimal high-order derivative estimates for the Lam\’{e} 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.

Speaker Profile：Haigang Li, Professor and Doctoral Supervisor at Beijing Normal University. His research focuses on the theoretical study of partial differential equations in materials science, achieving significant progress in areas such as the Babuska problem in composite materials, subwavelength resonance, and fluid-solid suspension problems. He has published over 50 papers in international mathematics journals including Math. Ann., Adv. Math., Arch. Ration. Mech. Anal., J. Math. Pures Appl., and Trans. AMS. He has received the Huo Yingdong Foundation Award from the Ministry of Education, the Second Prize in Natural Sciences from the Ministry of Education, and the Second Prize in Natural Sciences from the Beijing Municipal Government.

Faculty and students are welcome to attend!

Invited by: Huajun Gong

School of Mathematical Sciences

January 18, 2026