﻿ Mini Course on Wave Turbulence | Recent progress on mathematical theory of wave turbulence-求真书院

### Mini Course on Wave Turbulence | Recent progress on mathematical theory of wave turbulence

Abstract

The theory of wave turbulence is the statistical theory of interacting waves, or the wave analog of Boltzmann's kinetic theory. It started in the works of Peierls in the 1920s, and has had substantial developments in the 20th century, with significant applications in science. The mathematical study of this subject started with the early works of Spohn and Erdös-Yau et al. on linear models, and the nonlinear problem has recently attracted a lot of attention from the PDE community.In a sequence of papers published in the last few years, joint with Zaher Hani (University of Michigan), we have completely settled this full nonlinear problem, and established the rigorous mathematical foundation of the wave turbulence theory. In this mini-course, which contains four 2-hour lectures, I will briefly explain the scope of this subject, historical timeline, the recent works, and ideas involved in the proof. The first two lectures will focus on more general and intuitive descriptions of the theory, and the last two lectures will contain an overview of the important components of the proof.

Yu Deng 邓煜

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