应用数学系学术报告

--- 分析、偏微分方程与动力系统讨论班(2024秋季第1讲)

Almost sure global well-posedness for quadratic nonlinear Schrodinger system in 2-disc

孟繁飞 (启元实验室)

时间：9月25日(周三)上午 10:00-11:00

地点✷🏄🏻‍♂️：沙河主楼E602

摘要: We focus on the nonlinear Schrodinger equations on manifolds, and try to obtain their global solutions with low regularity. In this talk, I will introduce a system coupled by two quadratic nonlinear Schrodinger equations, and discuss its almost sure global well-posedness. The strategy is following Bourgain's step and to construct a probability measure which is invariant under the flow.

Our object is a Hamiltonian system, so Gibbs measure is a suitable choice which is defined for the entropy of ensemble in statistical mechanics. In the end of this talk, I will show the difficulty in the study of cubic nonlinear Schrodinger equation on 2-sphere which is related to some works of Burq-Gérard-Tzvetkov.

报告人简介: 孟繁飞，启元实验室助理研究员。2022年获中国工程物理研究院博士学位，研究方向是随机偏微分方程。主要关心哈密顿型色散方程的长时间动力学，特别是流形上的非线性薛定谔方程🧑🏽‍🚒，以及Gibbs测度在随机初值问题的应用🏇🏽。已在CVPDE🤾🏽‍♀️、JDE等期刊上发表数篇文章。

邀请人🤽🏻‍♀️：郑孝信

欢迎大家参加🍠！