At 9 o'clock in the morning on June 4, the 2021 "Famous Teachers' Lecture Hall" series of lectures co-sponsored by the School of Mathematical Sciences and the Institute of Applied System Analysis of Jiangsu University started on the cloud as scheduled. The guest speaker invited in this issue is the top expert in the field of international nonlinear analysis and partial differential equations—Professor Li Yanyan, a distinguished professor from the Department of Mathematics of Rutgers University and Director of the Center for Nonlinearity. More than 120 teachers and students attended the lecture, including Professor Guixiang Xu from Beijing Normal University, Professor Renhao Cui from Harbin Normal University, Professor Anmin Mao from Qufu Normal University, Professor Jingshi Xu from Guilin University of Electronic Technology, Professor Weisheng Niu from Anhui University, Professor Yansheng Zhong from Fujian Normal University, Professors Zhitao Zhang and Jun Wang from Jiangsu University.

Before the start of the lecture, Zhang Zhitao, Dean of the Academy of Mathematics, Jiangsu University, briefly introduced Professor Yanyan Li and presided over the lecture.

Professor Yanyan Li gave a wonderful academic report on the topic of "Regular solutions of the stationary Navier-Stokes equations on high dimensional Euclidean space", mainly explaining the regularity of weak solutions of static incompressible Navier-stokes equations in high dimensional space. First, he used the Galerkin method to illustrate the existence of weak solutions, and explained the research history of the regularity of weak solutions in low-dimensional spaces. Secondly, he introduced the latest research results on weak solutions of Navier-stokes equations in high-dimensional spaces, and elaborated on the proof idea: By first rewriting the Navier-stokes equation into a certain integral form of equation, then giving the proof of the prior estimation in the regularity theory, and finally using the classic Leray-Schauder degree theory to obtain the existence of smooth weak solutions.

In the report, Professor Li analyzed the profound connection between the Navier-stokes equation in mathematics and the classical functional theory, reflecting his profound mathematical skills. Professor Li's research work aroused great interest among teachers and students present. After the report, Professor Li gave patient and detailed answers to the mathematics questions that everyone was concerned about, and the teachers and students on the scene benefited a lot. Finally, Dean Zhang Zhitao made a concluding speech for the lecture.

The “Lecture Hall of Famous Teachers” brand activity established by our school aims to regularly invite well-known experts, academic authorities, and outstanding young scholars in the subject field to give lectures, continuously improve the mathematical literacy and scientific research and innovation capabilities of graduate students, strengthen exchanges and cooperation between scholars, and further enhance the academic influence of the subject.