Published on Department of Mathematics Calendar (https://calendar.math.yale.edu)

Week of May 1, 2023

May 4, 2023
Analysis [3]	Soliton resolution for nonlinear Schr\”odinger type equations	Xiaoxu Wu - Rutgers University	4:00pm -

May 11, 2023
Analysis [3]	Damped waves with singular damping on manifolds	Ruoyu P. T. Wang - Northwestern University	4:00pm -

Abstracts

Week of May 1, 2023

May 4, 2023
Analysis [3]	Soliton resolution for nonlinear Schr\”odinger type equations	4:00pm -	In this talk, I will discuss recent progress in our understanding of the long-term behavior of large solutions to nonlinear Schr\”odinger-type equations. Dispersive estimates are a crucial tool in studying nonlinear Schr\”odinger equations, and examples include Strichartz estimates and local decay estimates. I will also cover a new technique for proving local decay estimates that allows for the establishment of Strichartz estimates (global in time) when the potential is quasi-periodic in time and localized in space, in five spatial dimensions. This talk is based on a series of collaborative works with Avy Soffer.

May 11, 2023
Analysis [3]	Damped waves with singular damping on manifolds	4:00pm -	We will discuss a new damped wave semigroup for damping exhibiting H\”{o}lder-type blowup near a hypersurface of a compact manifold. We will use this semigroup to prove a sharp energy decay result for singular damping on the torus, where the optimal rate of energy decay explicitly depends on the singularity of the damping. We also show that no finite time extinction could happen under this setting. This is a joint work with Perry Kleinhenz.

Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2023-W17 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2023-W19 [3] https://calendar.math.yale.edu/seminars/analysis [4] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2023-W17 [5] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2023-W19