Normal form methods and low regularity solutions for fluid models

Waves, gravitation and geometry

The seminar will meet in Jingzhai (静斋) 105, Tsinghua University. In this seminar, we will study wave equations particularly nonlinear wave equations, from a geometric perspective, and inspired by the dynamics in general relativity. Among the topics ofinterest are black holes, stability, long-term dynamics,low-regularity, fluids, and shocks. We will have a combination of external and local speakers, including students.

Organizer：

Lars Andersson

Speaker：

Albert Ai (Peking University)

Time：

Wed., 10:15 am-12:00 pm, Mar. 19, 2025

Venue：

Jingzhai 105

Online：

Zoom Meeting ID:518 868 7656

Password: BIMSA

Title：

Normal form methods and low regularity solutions for fluid models

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.