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应用数学系

赵泽华 职称：准聘教授 电子邮箱：zzh at bit.edu.cn, zzhnkujhu at gmail.com

赵泽华是完美体育平台官网教授、博士生导师，于2021年夏加入完美体育平台官网工作。在此之前，分别于美国约翰霍普金斯大学（2014年秋-2019年夏）和马里兰大学（2019年秋-2021年夏）做博士和博后，合作导师为B. Dodson, M. Machedon, M. Grillakis等著名数学家；长期从事偏微分方程领域的研究，具体来说，分别为色散方程、多体问题及随机色散方程这几个方向，已完成学术论文30余篇，相关研究成果发表于Comm. Math. Phys., Peking Math J., SIAM J. Math. Anal., Ann. Henri Poincaré, Comm. Partial Differential Equations, J Funct. Anal., Int. Math. Res. Not.等国际权威学术期刊，受到了M. Christ, B. Schlein, M. Röckner等著名数学家的引用或好评；担任美国《数学评论》(Mathematical Reviews)评论员、德国《数学文摘》(Zentralblatt MATH)评论员、国家英才计划导师以及多个国家部门专家库专家；主持国家自然科学基金等项目多项；于2022年入选国家高层次人才计划（青年项目），于2023年获海淀青年科学家称号。教学方面：2024年获青教赛一等奖（学院）；主持教育教学改革项目多项；担任2024级数学强基班班主任；主讲未来精工班数学分析国际化课程，等等。社会任职：中国民主同盟完美体育平台官网良乡支部副主委；参与各级统战部、民盟、团委、工会等部门的调研、实践活动多次。如果有对我的科研方向感兴趣的同行、朋友、学生，非常欢迎与我联系！

教育背景

► 09/2014--06/2019, 数学博士，约翰霍普金斯大学（Johns Hopkins University）. 导师：Benjamin Dodson教授。

► 09/2010--06/2014, 数学学士（伯苓班），南开大学

工作经历

2022年10月-至今: 完美体育平台官网，准聘教授、博士生导师、青年领军人才

2021夏-2022年10月: 完美体育平台官网，副研究员

2019-2021夏：美国马里兰大学，诺维科夫博后，博后导师：Matei Machedon教授和 Manoussos Grillakis教授

研究方向

色散方程，随机色散方程，多体问题，调和分析。

代表论著

五年内部分学术代表作：

[1] Z. Zhao, Global well-posedness and scattering for the defocusing cubic Schrődinger equation on waveguide R²×T², Journal of Hyperbolic Differential Equations, Vol. 16, No. 1 (2019) 1-57.

[2] C. Gao and Z. Zhao, On scattering for the defocusing high dimensional inter-critical NLS, Journal of Differential Equations, Volume 267, Issue 11, Pages 6198-6215.

[3] X. Cheng, Z. Guo, and Z. Zhao, On scattering for the defocusing quintic nonlinear Schrődinger equation on the two dimensional cylinder, SIAM Journal on Mathematical Analysis, 52 (2020), no. 5, 4185-4237.

[4] X. Cheng Z. Zhao and J. Zheng, Well-posedness for energy-critical NLS on waveguide manifold, Journal of Mathematical Analysis and Applications, Volume 494, Issue 2, 15 February 2021.

[5] Z. Zhao, On scattering for the defocusing nonlinear Schrődinger equation on waveguide R^m×T (when m=2,3), Journal of Differential Equations, Volume 275, 25 February 2021, Pages 598-637.

[6] C. Fan and Z. Zhao, Decay estimates for nonlinear Schrődinger equations, Discrete Contin. Dyn. Syst., 41 (2021), no. 8, 3973-3984.

[7] X. Yu, H. Yue, Z. Zhao, Global well-posedness for the focusing, cubic NLS on product space R×T³, SIAM Journal on Mathematical Analysis, Vol. 53, Issue. 2; Pages. 2243-2274.

[8] Z. Zhao and J. Zheng, Long time dynamics for defocusing cubic NLS on three dimensional product space, SIAM Journal on Mathematical Analysis, Vol. 53, No. 3, pp. 3644-3660.

[9] J. Chong, M. Grillakis, M. Machedon and Z. Zhao, Global estimates for the Hartree-Fock-Bogoliubov Equation, Communications in Partial Differential Equations, 46 (2021), no. 10, 2015–2055.

[10] J. Chong and Z. Zhao, Dynamical Hartree-Fock-Bogoliubov Approximation of Interacting Bosons, Ann. Henri Poincaré, 23 (2022), no. 2, 615–673.

[11] C. Fan and Z. Zhao, A note on decay property of nonlinear Schrődinger equations, Proceedings of AMS, Volume 151, Number 6, June 2023, Pages 2527–2542..

[12] X. Yu, H. Yue, Z. Zhao, On the decay property of cubic fourth order Schrődinger equation, Proceedings of AMS, Volume 151, Number 6, June 2023, Pages 2619–2630.

[13] K. Yang and Z. Zhao, On scattering asymptotics for the 2D cubic resonant system, Journal of Differential Equations, Vol. 345, 5 February 2023, Pages 447-484.

[14] Q. Su and Z. Zhao, Dynamics of subcritical threshold solutions for energy-critical NLS, Dynamics of Partial Differential Equations, Vol. 20, No. 1 (2023), pp. 37-72.

[15] Y. Sire, X. Yu, H. Yue and Z. Zhao, Singular Levy processes and dispersive effects of generalized Schrődinger equations, Dynamics of Partial Differential Equations, Volume 20, Number 2, 2023, Pages: 153-178.

[16] C. Fan, W. Xu and Z. Zhao, Long time behavior of stochastic NLS with a small multiplicative noise, Communications in Mathematical Physics, Volume 404, pages 563-595 (2023).

[17] X. Yu, H. Yue and Z. Zhao, Global well-posedness and scattering for fourth order Schr\"odinger equation on waveguide manifold, SIAM Journal on Mathematical Analysis, Volume 56, Iss. 1 (2024).

[18] C. Fan, G. Staffilani and Z. Zhao, On decaying properties of nonlinear Schr\"odinger equations, SIAM Journal on Mathematical Analysis (2024).

[19] X. Yu and Z. Zhao, On scattering for NLS on waveguide manifolds: a short survey, Birkh\"auser Series: Research Perspectives Ghent Analysis and PDE Center (2024).

[20] C. Fan and Z. Zhao, On long time behavior for stochastic nonlinear Schr\"odinger equations with a multiplicative noise, International Mathematics Research Notices (2024).

[21] X. Huang, X. Yu, Z. Zhao and J. Zheng, On Strichartz estimate for many body Schr\"odinger equation in the periodic setting, Forum Mathematicum (2024).

[22] T. Ma, H. Wang, X. Yu and Z. Zhao, On the decaying property of quintic NLS on 3D hyperbolic space, Nonlinear Analysis, Theory, Methods and Applications (2024).

[23] Y. Deng, C. Fan, K. Yang, Z. Zhao and J. Zheng, On bilinear Strichartz estimates on waveguides with applications, Journal of Functional Analysis (2024).

[24] J. Chong, X. Dong, M. Grillakis, M. Machedon and Z. Zhao, Global uniform in N estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the case beta<1, Peking Mathematical Journal. (2024)

其他成果及预印本结果见arXiv.

Personal page: https://sites.google.com/view/zehuazhao/home