School of Mathematical Sciences Academic Report [2023] No. 015  

(High-Level University Construction Series Report No. 1038)  

Lecture Title: Singularity Formation of (n + 1)-Dimensional Compressible Euler Equations with Free Boundary

Speaker: Dr. Manwai YUEN (Education University of Hong Kong)  

Date & Time: 3:00–4:00 PM, Thursday, March 20, 2025  

Venue: Room 207, Zhizhi Building, Shenzhen University  

Abstract: Here, we consider the general (N + 1)-dimensional compressible Euler equations with a free boundary (System A) and obtain that the classical solutions cannot survive after a finite time for all N. More specifically, for initial data with compactly supported density and without any symmetry assumptions, we show that the classical solutions to system A blow up in finite time by considering a general class of C2 positive test functions f(x) satisfying ∆f(x) = λf(x).

Biography: Dr. Manwai YUEN has been an assistant professor since 2014 in the Department of Mathematics and Information Technology at the Education University of Hong Kong, and as a lecturer in 2011-14. Dr. Yuen's research interest is applied analysis of nonlinear partial differential equations, specially involving blowup phenomena and similar solutions. Dr. Yuen's 73 journal papers (with 66 SCI or SCIE) were published by 36 international Math and Physics journals. His published papers have accumulated 563 citations and a H-index 13 from Scopus.

All faculty and students are welcome to attend!

Invited by: Huang Jiaxing

School of Mathematical Sciences  

March 17, 2025