Strichartz estimates for the Schrödinger equation on the sphere

发布时间：2025-07-02 作者：浏览次数：

Speaker:	黄晓琦	DateTime:	2025年7月10日（周四）上午10:00-11:00
Brief Introduction to Speaker: Xiaoqi Huang（黄晓琦） is an Assistant Professor in the Department of Mathematics at Louisiana State University. His research focuses on harmonic analysis and its applications to partial differential equations. He has published work in journals such as Invent. Math., the American Journal of Mathematics, Journal of the European Mathematical Society, Communications in Mathematical Physics, and Journal of Functional Analysis, among others.		Place:	国交2号楼315会议室
Abstract:We will discuss optimal space-time estimates in $L^q_{t,x}$ spaces for solutions to the Schrödinger equation on the standard round sphere, which is related to the results of Burq, Gérard and Tzvetkov (2004). The proof is based on the arithmetic properties of the spectrum of the Laplacian on the sphere, as well as local bilinear oscillatory integral estimates in harmonic analysis, which allow us to relate the problem to Strichartz estimate on one-dimensional tori. This is based on joint work with Christopher Sogge.