报告题目：Normalized ground states for the mass supercritical Schrödinger-Bopp-Podolsky system: existence, uniqueness, limit behavior, strong instability

报告人：黄娟 教授（四川师范大学）

邀请人：张华丽

时间地点：2025年2月28日周五下午16:00-17:00 腾讯会议805208344

摘要：This talk concerns the normalized ground states for the nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics. This equation has a nonlocal nonlinearity and a mass supercritical power nonlinearity, both of which have deep impact on the geometry of the corresponding functional, and thus on the existence, limit behavior and stability of the normalized ground states. In the present study, the existence of critical points is obtained by a mountain-pass argument developed on the L2-spheres. To be specific, we show that normalized ground states exist, provided that spherical radius of the L2-spheres is sufficiently small. Then, by discussing the relation between the normalized ground states of the Schrödinger-Bopp-Podolsky system and the classical Schrödinger equation, we show a precise description of the asymptotic behavior of the normalized ground states as the mass vanishes or tends to infinity. Moreover, we discuss the radial symmetry and uniqueness of the normalized ground states. Finally, the strong instability of standing waves at the mountain-pass energy level is studied by constructing an equivalent minimizing problem. Also, as a byproduct, we prove that the mountain-pass energy level gives a threshold for global existence based on this equivalent minimizing problem.

个人简介：黄娟， 教授，博士生导师，四川省海外高层次留学人才。先后主持国家自然科学基金项目3项，四川省科技厅基金项目2项，四川省教育厅青年基金项目1项。先后入选四川师范大学“251重点人才工程”、四川师范大学“狮山学者 杰出青年学者”。相关研究成果已在JMP、DCDS等国际学术期刊上发表论文二十余篇。