报告人：徐桂香 教授
报告题目：Long time dynamics for the focusing, energy-critical Hartree equation
报告时间：2023年12月14日9:30-10:30
邀请人：王智勇、唐兴栋
报告地点：藕舫楼704
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报告摘要：
In this report, we consider long time dynamics of radial threshold solutions for the focusing, generalized energy-critical Hartree equation and classify all radial threshold solutions. The main arguments are the spectral theory of the linearized operator, the modulation analysis and the concentration compactness rigidity argument developed by T. Duyckaerts and F. Merle to classify all threshold solutions for the energy critical NLS and, later by D. Li and X. Zhang in higher dimensions. The new ingredient here is to solve the nondegeneracy of ground state with nonlocal structure in the energy space by the nondegeneracy result of ground state in the bound space and the Moser iteration method. It is a joint work with X. Li, C. Liu, X. Tang.
报告人简介：
徐桂香，北京师范大学数学统计学院教授，主持和参与了多项国家自然科学基金重点项目、面上项目多项。在位势波动方程孤子猜想、导数NLS方程多孤子解的稳定性、耦合非线性相互作用薛定谔方程解的整体适定性与散射、Hartree方程解长时间动力学行为、高阶能量临界NLS方程解的整体适定与散射、质量临界NLS及KdV方程解的低正则性理论等方面做出重要研究成果。系列论文发表在Amer. J. Math., Comm. Math. Phys.,J. Funct. Anal., J. Math. Pures Appl. , Ann I. H. Poincaré, AN. , IMRN, Comm. PDEs. , SIAM J. Math. Anal.，CVPDE等学术期刊上。
数学与统计学院
2023年12月7日