数学研究所
数学科学全国重点实验室
学术报告
偏微分方程讨论班
Speaker: 邵城阳（IHES）
Inviter: 范晨捷
Language: Chinese
Title: Paradifferential calculus and its application to oscillatory motions ( part I)
Time&Venue: 2025年7月15日（星期二）10:00-11:00& 思源楼S813
Abstract:I will explain how Bony’s paradifferential calculus can be applied to study differential equations that describe oscillatory motions. After a quick, black-box style introduction to paradifferential and paracomposition operators, I will present the paradifferential approach to classical KAM theory and “KAM for PDEs”. In other words, it will be discussed how the traditional Nash-Moser iteration can be replaced by a fixed point argument in the construction of quasi-periodic solutions to classical Hamiltonian systems or dispsersive/hyperbolic differential systems. Preliminaries will be kept minimal: only some basic knowledge of Fourier analysis (Littlewood-Paley decomposition and function spaces) will be needed.
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