报告题目 Title：Self-Similar Solutions to the Stationary Navier-Stokes Equations

报告人 Speaker：Jeaheang Bang

报告人所在单位 Affiliation：Westlake University

时间 Time：2025-10-31 15:00-16:00

地点 Venue：Room 2001, Guanghua Eastern Main Tower, Fudan University (Handan Campus)

报告摘要 Abstract：The study of self-similar solutions plays an important role in understanding the regularity theory or the asymptotic behaviors of a solution to the Navier-Stokes equations. We have been studying it for the stationary Navier-Stokes equations in various dimensions $n=2$ or $n\geq 4$ in domains with or without boundary. When $n\geq 4$, we proved that any steady solution satisfying $|u(x)|\leq C/|x|$ in $\mathbb{R}^n\setminus \{0\}$ must be trivial. Neither smallness assumptions on $C$ nor self-similarity assumptions on $u$ are required. When $n=2$, we studied this topic in a sector with the no-slip boundary condition and established necessary and sufficient conditions in terms of the angle of the sector and the flux to guarantee the existence of self-similar solutions of a given type. In addition, we investigated uniqueness and non-uniqueness of flows with a given type. Our main idea for the higher dimensional result is to use weighted energy estimates and the equation of the head pressure. For the two-dimensional result, we used detailed properties of complete and incomplete elliptic functions. These are joint works with Changfeng Gui and Hao Liu (U. of Macau), Chunjing Xie (Shanghai Jiao Tong University), and Yun Wang (Soochow University).

个人简介 Bio：Jeaheang (Jay) Bang earned his Ph.D. from Rutgers University-New Brunswick in 2021 under the supervision of Yanyan Li. He worked as a postdoctoral scholar at the University of Texas at San Antonio with his mentor Changfeng Gui from 2021 to 2023, and as a visiting assistant professor at Purdue University in Spring 2024 before joining the Institute for Theoretical Sciences, Westlake University as a postdoctoral scholar in September 2024.

海报 Poster：Jeaheang Bang 学术报告.jpg