数学研究所

数学科学全国重点实验室

学术报告

偏微分方程研讨班

Speaker: 邵城阳（IHES）

Inviter: 范晨捷

Language: Chinese

Title: Paradifferential calculus and its application to oscillatory motions, part II

Time&Venue: 2025年7月22日（星期二）10:00-11:00& 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.

-------------------------------------------------------------------------------------

Speaker: 邵城阳（IHES）

Inviter: 范晨捷

Language: Chinese

Title:  Paradifferential calculus and its application to oscillatory motions, part III

Time&Venue: 2025年7月29日（星期二）10:00-11:00& 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.