题目：Wellposedness for the KdV hierarchy
摘要：The KdV hierarchy is a hierarchy of integrable equations generalizing the KdV equation. In this talk, we show that the whole hierarhcy is wellposed for initial data in H^{-1} on the line, while on the torus we have wellposedness in H^{N-2} for N-th KdV equation. The main ingredients include: (1) modified Muria map that relate the KdV hierarchy to the Gardner hierarchy; (2) the idea of approximate flow by Killip and Visan (3) Kato smoothing estimate for KdV hiearchy and the difference flow on the line. This is based on joint work with F. Klaus and H. Koch.
时间：2024年1月2日下午15:00
地点：9001诚信金沙中关村校区教学楼N106
主持人： 王东教授
报告人简介：刘保平，现任北京大学数学科学院副教授，国家级青年人才计划入选者。2012年于加州伯克利大学获博士学位，师从著名数学家 Daniel Tataru，后在芝加哥大学做博士后，导师为国际数学联盟主席Kenig和著名数学家Wilhelm Schlag。刘保平博士的研究领域为非线性色散方程，研究成果发表在 Amer. J. Math，IMRN，Advances in Math，Comm. Math. Phys, J. Funct. Anal.等国际著名学术期刊。
