学术报告

题      目：Gibbs Dynamics for the Weakly Dispersive Nonlinear Schrödinger Equations

报  告  人：王玉昭  副教授  (邀请人：李颖花 )

                                   英国伯明翰大学

时      间：7月1日  10：00-11：00

地     点：数科院东楼421

报告人简介:

        主要研究调和分析与偏微分方程，曾任华北电力大学数理学院副教授，现任伯明翰大学数学学院副教授。其主要研究领域是非线性色散偏微分方程（PDEs）的数学分析、谐波分析、概率论和动力系统。他对Strichartz估计及其在离散非线性偏微分方程中的应用、非线性离散偏微分方程的概率和应用于非线性离散偏微分方程的方式方法有较好的研究成果。

摘      要：

       In this talk, I will explain the existence of global strong solutions with flow property to the fractional NLS for the whole weakly dispersive range \alpha > 1. To prove this result, we employed Deng-Nahmod-Yue's random averaging operator method. To cover the full range \alpha > 1, we prove several sharp fractional counting estimates. We then used the idea of  the random matrix, which improves the multilinear estimates. We also used several crucial observations, such as the unitary of the random average operator, the non-resonance structure, and the Gamma condition. This is a joint work with Rui Liang.