Zu Chongzhi Mathematics Research Seminar

Date and Time (China standard time): Tuesday, March 18, 4:30 pm – 5:30 pm

Location: WDR 1007

Zoom: 937 4819 2342, Passcode: dkumath

Title: Self-Similar Solutions to the Stationary Navier-Stokes Equations in a Higher Dimensional Cone

Speaker: Jeaheang Bang

Abstract: Self-similar solutions play an important role in understanding the regularity and asymptotic behavior of solutions to the Navier-Stokes equations. We recently showed that axisymmetric self-similar solutions to the stationary Navier-Stokes equations in an $n$-dimensional cone with the no-slip boundary condition except at the origin must be trivial when $n\geq 3$. It rules out this particular scenario of boundary singularity, which has finite Dirichlet energy when $n\geq 5$. The main idea is to apply ODE techniques along with a sign property of the head pressure. This is a joint work with Changfeng Gui, Chunjing Xie, Yun Wang, and Hao Liu.

Bio: Jeaheang Bang received a PhD at Rutgers University in 2021 under the supervision of Yanyan Li, and he is now serving as a postdoc in the research group of Alexey Cheskidov. His research interests lie in fluid mechanics and PDEs.