Scaling limit of modulation spaces and their applications

：王保祥（集美大学）
：2022-07-05 10:30
：厦大海韵园实验楼105报告厅

报告人：王保祥（集美大学）

时  间：7月5日上午10:30

地  点：厦大海韵园实验楼105报告厅

内容摘要:

Modulation spaces Msp,q were introduced by Feichtinger in 1983. Benyi and Oh in 2020 defined a modified version to Feichtinger's modulation spaces for which the symmetry scalings are emphasized for its possible applications in PDE. By carefully investigating the scaling properties of modulation spaces and their connections with Benyi and Oh's modulation spaces, we introduce the scaling limit versions of modulation spaces, which contains both Feichtinger's and Benyi and Oh's modulation spaces.   As their applications, we will give a local well-posedness and a (small data) global well-posedness results for nonlinear Schrodinger equation in some scaling limit of modulation spaces, which generalize the well posedness results on modulation spaces and certain super-critical initial data in Hs or in Lp are involved in these spaces. This is a joint work with M. Sugimoto.

个人简介：

王保祥，1993年获得北京应用物理与计算数学所博士学位，从师郭柏灵院士、孙和生教授。现任集美大学理学院特聘教授，主要从事调和分析空间理论和非线性偏微方程的研究。王保祥解决了Navier-Stokes方程的在端点临界Besov空间的不适定性的长期公开问题，开创了频率一致分解方法研究非线性发展方程。研究工作获得了国际上一些著名专家很高的评价。

 

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