Academic Report of School of Mathematical Sciences [2026] No. 095

(Series Report for High-Level University Construction No. 1354)

Title：Global Existence of Smooth Solutions to the Incompressible Navier-Stokes Equations

Speaker：Professor Zhou Yong (Wenzhou University)

Time：14:55-16:30, Oct. 22, 2026

Location：Tencent Meeting:138298910

Abstract: This report primarily explores the global existence of smooth solutions to the classical and generalized incompressible Navier-Stokes equations. Key topics include the local existence of smooth solutions, the global existence of weak solutions, and the issue of smooth solutions blowing up in finite time, as recently highlighted by OpenAI. The talk will also discuss the global existence of smooth solutions under certain conditions—for example, when the exponent of the fractional derivative representing viscous diffusion in the generalized Navier-Stokes equations is sufficiently large, or when the damping term in the Navier-Stokes equations with a damping term is sufficiently large. This talk is primarily a review and will present several open problems and conjectures.

Speaker Profile：Zhou Yong is an Oujiang Distinguished Professor at Wenzhou University and has been repeatedly named a “Highly Cited Researcher” by Thomson Reuters and ranked among the top 2% of scientists worldwide. Professor Zhou Yong has received the Zhong Jiaqing Mathematics Award from the Chinese Mathematical Society, the Shanghai Mayor’s Award for Scientific and Technological Innovation, the Zhejiang Provincial Youth Science and Technology Award, and the Ministry of Education’s Huo Yingdong Young Teacher Fund Award, among other honors. He has been selected for several talent support programs, including the Ministry of Education’s New Century Excellent Talents Support Program, the Shanghai Dawn Program, and the Morning Star Program. He has long served on the editorial boards of international journals such as BMMS (JCR Q1).

Faculty and students are welcome to attend!

Invited by: Duan Qin

School of Mathematical Sciences

October 19, 2026