当前位置: 首 页 - 科学研究 - 学术报告 - 正文

304am永利集团、所2022年系列学术活动(第143场):Yao Yao 教授 National University of Singapore

发表于: 2022-09-16   点击: 

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.