Long Feng Science Forum Seminar Series | Seminar #85

Dear All,

You are cordially invited to the eighty-fifth seminar of Long Feng Science Forum Seminar Series. It will be delivered by Dr. Yongming LUO (Shenzhen MSU-BIT University) at 4:30 pm on September 26 (Tuesday). This seminar will discuss "Almost Sure Scattering for the Defocusing Cubic Nonlinear Schrödinger Equation on R3T1".

Seminar Information

Time & Date: 4:30 - 5:30 PM on September 26 (Tuesday), Beijing Time

Venue: Room 208, Cheng Dao Building

Speaker: Dr. Yongming LUO, Shenzhen MSU-BIT University

Host: Prof. Yuan CHEN, The Chinese University of Hong Kong, Shenzhen

Abstract: 

We consider the Cauchy problem for the defocusing cubic nonlinear Schrödinger equation (NLS) on the waveguide manifold R3T1 and establish almost sure scattering for random initial data. Different from the classical models, we encounter in this setting some new difficulties due to the mixed nature of the waveguide domain. The main new ingredient is a layer-by-layer refinement of the newly established randomization introduced by Shen-Soffer-Wu, which enables us to also obtain strongly smoothing effect from the randomization for the forcing term along the periodic direction. To our knowledge, the paper also gives the first almost sure well-posedness result for NLS on product spaces.

Biography

Yongming Luo obtained his Ph.D. degree in Mathematics at the University of Kassel in 2019 and worked as a postdoctoral associate at the Technical University in Dresden from 2020 to 2022. As of March 2023, he becomes a Senior Lecturer of the Faculty of Computational Mathematics and Cybernetics at the Shenzhen MSU-BIT University. Yongming Luo is mainly interested in the research area mathematical analysis, where calculus of variations and harmonic analysis play a fundamental role. Recently, Yongming Luo has also made some significant contributions to the study of nonlinear Schrödinger equations and his recent works in this direction have already been accepted by world renowned journals such as Journal de Mathématiques Pures et Appliquées, Annales de l'Institut Henri Poincaré C, Journal of Functional Analysis and Mathematische Annalen.

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