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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
Andrew Schopieray
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
I grew up in a rural area in northern Michigan and did not consider mathematics as a career until I was in my 20's; I cooked professionally for about 10 years. I've since earned degrees in the states of Michigan, Oregon, and Washington, and done postdoctoral research in Australia, Canada, and the United States. My research will probably stay related to tensor categories and their many applications, but I will always think about whatever problems seem interesting to me in the moment. I am a year-round alpine climber, and an avid wildlife photographer.