Distinguished Lecture——The Korteweg-de Vries hierarchy at low regularity
报告人：Herbert Koch (University of Bonn)
时间：2024-09-13 16:00-17:00
地点：智华楼四元厅
Abstract: The Korteweg-de Vries equation is closely related to the Schroedinger operator. I will explain this relation and some of its consequences, including the Miura map, which relates the KdV hierarchy to the slightly simpler Gardner hierarchy, the generating function for the Hamiltonians and its role for the commuting vector field method of Killip and Visan for the whole hierarchy, which includes equations of any odd order. In particular the whole hierarchy is wellposed in H^{-1}(R) in the sense that there exist unique weak solutions for initial data in H^{-1}.
个人简介：Herbert Koch是德国波恩大学数学系教授，国际著名的调和分析与微分方程专家。主要研究领域包括调和分析、色散方程和流体方程解的适定性理论和长时间行为。他和Daniel Tataru关于Navier-Stockes 方程解的适定性结果是这一个领域的里程碑式的结果，被国际数学界称为Koch-Tataru解；他们引入的有界变差空间对偶空间理论成为现代调和分析以及非线性色散方程理论的一个重要的工作空间，为很多非线性问题的研究提供了新途径。Herbert Koch教授在包括Publ. Math. IHES, Duke Math, CPAM, JEMS在内的顶尖数学杂志上发表论文90余篇。
