**Zu Chongzhi Mathematics Research Seminar**

**Date and Time (China standard time): **Thursday, October 19, 10:00 am-11:00 am

**Location:** WDR 1007

**Zoom: **919 3182 3019;** Passcode: **dkumath

**Title**: On nonlinear instability of liquid Lane-Emden stars

**Speaker**: Shuang Miao

**Bio**: Shuang Miao is a Chinese mathematician who works as Professor of Mathematics at Wuhan University. His research work involves the mathematical theory of hyperbolic partial differential equations. He earned bachelor’s degree in 2008 from Wuhan University and completed his doctorate in 2013 from Chinese Academy of Sciences. During his Ph.D study he worked as research assistant at ETH Zurich in 2011-2012. After temporary positions at University of Michigan and EPF Lausanne, he became a professor at Wuhan University in 2019. He won the Qiu Shi Outstanding Young Scholar Prize in 2020, the Henry Fok Prize for Young Scientists (2nd rank) in 2022, and the ICCM Silver Medal in Mathematics in 2022 “for his important contributions to nonlinear partial differential equations arising from fluid dynamics and general relativity”.

**Abstract**: In this talk I will present our recent work on dynamical nonlinear instability of liquid Lane-Emden stars in $\bbR^{3}$ whose adiabatic exponents take values in $[1,\frac43)$. Our proof relies on a priori estimates for the free boundary problem of a compressible self-gravitating liquid, as well as a quantitative analysis of the competition between the fastest linear growing mode and the source. This is joint work with Zeming Hao.