BIMSA >
Waves, gravitation and geometry
Waves, gravitation and geometry
Normal form methods and low regularity solutions for fluid models
Normal form methods and low regularity solutions for fluid models
Organizers
Lars Andersson
,
Haiming Du
, Pin Yu
Speaker
Albert Ai
Time
Wednesday, March 19, 2025 10:15 AM - 12:00 PM
Venue
Jingzhai-105
Online
Zoom 518 868 7656
(BIMSA)
Abstract
In this talk, we consider the Cauchy problem for families of dispersive fluid models, including dispersive generalizations of the Benjamin-Ono equation and surface quasi-geostrophic (SQG) equation. A key property of both of these models is a null structure in the nonlinearity, which in particular implies the availability of a normal form transformation which can lessen impact of the nonlinearity. We discuss how paradifferential analysis allows the application of normal forms in the setting of these quasilinear fluid models. This talk discusses joint work with Grace Liu and Ovidiu-Neculai Avadanei.
Speaker Intro
Albert Ai received his Bachelor's degree from Princeton University in 2013, and his PhD at the University of California, Berkeley in 2019, advised by Daniel Tataru. After holding a postdoctoral position at the University of Wisconsin-Madison, he is currently an assistant professor at BICMR. His research interests lie at the intersection of dispersive PDEs and harmonic analysis.