报告题目：Symmetry and uniqueness via a variational approach

报 告 人：Yao Yao 教授

所在单位：National University of Singapore

报告时间：2022年9月16日 14：00-15：00

报告地点：腾讯会议 946593821

校内联系人：魏元鸿 weiyuanhong@jlu.edu.cn

报告摘要：For some nonlocal PDEs, their steady states can be seen as critical points of some associated energy functional. Therefore, if one can construct perturbations around a function such that the energy decreases to first order along the perturbation, this function cannot be a steady state. In this talk, I will discuss how this simple variational approach has led to some recent progress in the following equations, where the key is to carefully construct a suitable perturbation.

I will start with the aggregation-diffusion equation, which is a nonlocal PDE driven by two competing effects: nonlinear diffusion and long-range attraction. We show that all steady states are radially symmetric up to a translation (joint with Carrillo, Hittmeir and Volzone), and give some criteria on the uniqueness/non-uniqueness of steady states within the radial class (joint with Delgadino and Yan). I will also briefly discuss applications of this variational approach to the 2D Euler equation (joint with Gómez-Serrano, Park and Shi) and a geometry problem (joint with Li and Yan).

报告人简介：Yao Yao is a Dean’s Chair Associate Professor at Department of Mathematics, National University of Singapore. She is interested in the mathematical analysis of nonlinear PDEs arising from fluid mechanics and mathematical biology.