Symmetry and Uniqueness in Nonlocal PDEs - A Variational Approach

Explore the intricacies of nonlocal PDEs and their steady states in this seminar presented by Yao Yao from the National University of Singapore. Delve into the variational approach for analyzing symmetry and uniqueness in aggregation-diffusion equations and 2D Euler equations. Learn how carefully constructed perturbations can lead to insights on radial symmetry, uniqueness, and non-uniqueness of steady states. Discover recent progress in understanding stationary and uniformly-rotating solutions, including the settlement of open questions on rotating patches and the radial symmetry of smooth stationary solutions with compactly supported, nonnegative vorticity. Gain valuable knowledge on advanced mathematical concepts and their applications in industrial and applied mathematics during this 71-minute presentation, part of the Society for Industrial and Applied Mathematics' Seminar in the Analysis and Methods of PDE series.