Speaker: Prof.Herbert Koch，University of Bonn, Germany

Inviter: 张翼副研究员

Title: The Korteweg-de Vries Hierarchy at Low Regularity

Language: English

Time & Venue: 2024.09.17 09:00-09:50 N219 Zoom meeting: 878 4974 2364 Code: AMSS2024

Abstract: The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in L^2, and hence of the Korteweg-de Vries hierarchy in low regularity.