分析学研讨班
题目：Strichartz estimates for orthonormal systems on compact manifolds
报告人：张城（清华大学）
时间：2025年5月16日，10:00-11:00
地点：明德楼B201-1 报告厅
Zoom ID: 266 430 0366 密码: 1222
报告人简介：张城，清华大学数学中心助理教授，2021年入选海外高层次青年人才，研究方向是调和分析，主要研究流形上的特征值和特征函数估计及其在偏微分方程中的应用，部分科研成果发表在Camb. J. Math., Adv. Math, CMP, JMPA, APDE等国际一流期刊。
摘要：We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schrödinger equations. Our results generalize the classical (single-function) Strichartz estimates on compact manifolds by Kapitanski, Burq-Gérard-Tzvetkov, Dinh, and extend the Euclidean orthonormal version by Frank-Lewin-Lieb-Seiringer, Frank-Sabin, Bez-Lee-Nakamura. On the flat torus, our new results for the Schrödinger equation cover prior work of Nakamura, which exploits the dispersive estimate of Kenig-Ponce-Vega. We achieve sharp results on compact manifolds by combining the frequency localized dispersive estimates for small time intervals with the duality principle due to Frank-Sabin. We construct examples to show these results can be saturated on the sphere, and we can improve them on the flat torus by establishing new decoupling inequalities for certain non-smooth hypersurfaces. As an application, we obtain the well-posedness of infinite systems of dispersive equations with Hartree-type nonlinearity. This is joint work with Xing Wang (Hunan Univ.) and An Zhang (Beihang Univ.).
