清华主页 EN
导航菜单

周五现代数学报告:Symmetry and uniqueness via a variational approach

来源:清华大学丘成桐数学科学中心 05-25

时间:5月27日 16:00-17:00

地点:Zoom Meeting: 271 534 5558 Passcode: YMSC

组织者:Prof.Yao Yao(National University of Singapore)

主讲人:Prof.Yao Yao(National University of Singapore)

讲座提要:

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 discuss the 2D Euler equation, where we aim to understand under what condition must a stationary/uniformly-rotating solution be radially symmetric. Using a variational approach, we settle some open questions on the radial symmetry of rotating patches, and also show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial (joint with Gómez-Serrano, Park and Shi).




主讲人介绍:

Yao Yao is currently an Associate Professor of Mathematics at the National University of Singapore. She received her BS degree from Peking University in 2007, and PhD degree in 2012 from UCLA. She was a Van Vleck Visiting Assistant Professor at University of Wisconsin-Madison in 2012-2015, and an Assistant Professor at Georgia Institute of Technology in 2015-2021. Her research focuses on the analysis of partial differential equations arising in mathematical biology and fluid dynamics, especially on the equations with a nonlocal transport term. She was a recipient of the NSF CAREER Award in 2018 and Sloan Research Fellowship in 2020.

返回顶部
相关文章
  • Symmetry and uniqueness via a variational approach

    Abstract: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 ...

  • [YMSC-BIMSA Quantum Information Seminar] 30 Anchoring Variational Quantum Algorithms via Statistical Learning Theory

    摘要: Near-term quantum machines provide a novel way to explore many scientfic domains beyond the reach of classical machines. Meanwhile, near-term quantum machines are fragile, where the available quantum resources are limited and error-prone. Variational quantum algorithms (VQAs) are leading candidates to alleviate these defects. Experimental studies have demonstrated the potential of VQAs ...