刘保平 - 北京大学 - 北京国际数学研究中心

个人简介

I'm an associate professor at Beijing International Center for Mathematical Research at Peking University . Previously, I received my Bachelor's degree in math from Peking University in 2006. Then I went to University of California, Berkeley where I finished my Ph.D. working with Professor Daniel Tataru in 2012. From 2012-2015, I was an L.E. Dickson instructor at University of Chicago working with Professor Carlos Kenig and Wilhelm Schlag .

研究领域

I am interested in nonlinear partial differential equations arising from fluid mechanics and mathematical physics. The understanding of these problems requires combining ideas from different fields such as harmonic analysis, spectral theory, dynamical system, etc.

近期论文

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A General Scattering theory for Nonlinear and Non-autonomous Schroedinger Type Equations- A Brief description with Avy Soffer. arxiv preprint. On Threshold Solutions of equivariant Chern-Simons-Schrodinger Equation. with Zexing Li. Accepted by Annales de l'Institut Henri Poincare C , Analyse Non Lineaire.. Global center stable manifold for the defocusing energy critical wave equation with potential. with Hao Jia, Wilhelm Schlag, Guixiang Xu. Amer. J. Math. 142 (2020), no. 5, 1497-1557. Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case. with Hao Jia, Wilhelm Schlag, Guixiang Xu. International Mathematics Research Notices, Vol. 2017, No. 19, pp. 5977-6035 Stable soliton resolution for exterior wave maps in all equivariance classes. with Carlos Kenig, Andrew Lawrie, and Wilhelm Schlag, Advances in Mathematics 285 (2015) 235-300. Channels of energy for the linear radial wave equation. with Carlos Kenig, Andrew Lawrie, and Wilhelm Schlag, Advances in Mathematics 285 (2015) 877-936. Long time dynamics of defocusing energy critical 3 + 1 dimensional wave equation with potential in the radial case. with Hao Jia and Guixiang Xu, Communications in Mathematical Physics, Volume 339, Issue 2, pp 353-384. Global wellposedness of the equivariant Chern-Simons-Schroedinger equation.with Paul Smith, Revista Matematica Iberoamericana 32 (2016), no. 3, 751-794. Low regularity solution for Chern-Simons-Schrodinger equation.with Paul Smith, Daniel Tataru, International Mathematics Research Notices, Volume 2014, issue 23, pages 6341-6398. A-priori bounds for KdV equation below H^{-3/4}.Journal of Functional Analysis 268 (3), 501-554

学术兼职

Service Organize PDE/Analysis Seminar at BICMR, Peking University Sep 2015- present Organize Calderon Zygmund Analysis Seminar at University of Chicago Oct 2013 - June 2015 Instructor for Summer REU at U.Chicago in 2014 with topic Equilibria in Nonlinear Systems; Summer REU at U.Chicago in 2015 with topic Introduction to Wave equation Article referee for Discrete and Continuous Dynamical System - A(2), Communications in Mathematical Physics(2), Nonlinear Analysis Series B, Nonlinearity