BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yao Yao (National University of Singapore) DTSTART:20211202T163000Z DTEND:20211202T173000Z DTSTAMP:20260423T040037Z UID:SIAM-PDE/16 DESCRIPTION:Title: Symmetry and uniqueness via a variational approach\nby Yao Yao (Nati onal University of Singapore) as part of Seminar In the Analysis and Metho ds of PDE (SIAM PDE)\n\n\nAbstract\nFor 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 th at the energy decreases to first order along the perturbation\, this funct ion cannot be a steady state. In this talk\, I will discuss how this simpl e variational approach has led to some recent progress in the following eq uations\, where the key is to carefully construct a suitable perturbation. \n\nI will start with the aggregation-diffusion equation\, which is a non local PDE driven by two competing effects: nonlinear diffusion and long-ra nge attraction. We show that all steady states are radially symmetric up t o a translation (joint with Carrillo\, Hittmeir and Volzone)\, and give so me criteria on the uniqueness/non-uniqueness of steady states within the r adial class (joint with Delgadino and Yan). I will also discuss the 2D Eul er equation\, where we aim to understand under what condition must a stati onary/uniformly-rotating solution be radially symmetric. Using a variation al approach\, we settle some open questions on the radial symmetry of rota ting patches\, and also show that any smooth stationary solution with comp actly supported and nonnegative vorticity must be radial (joint with Góme z-Serrano\, Park and Shi).\n LOCATION:https://researchseminars.org/talk/SIAM-PDE/16/ END:VEVENT END:VCALENDAR