Existence and nonexistence results of nonlinear Dirac equations
主 讲 人 ：郭琪 讲师
活动时间：03月09日10时00分
地 点 ：腾讯会议 会议号：839392948
讲座内容：
Abstract: In this talk, we try to answer three questions about the existence and nonexistence of stationary solutions of nonlinear Dirac equations:
1. what if two components of spinors equal zero?
2. what happens when the frequency does not belong to the spectral gap (-mc^2,mc^2)?
3. does there exist a general method to show nonexistence of ground states with holonomic constraints?
These questions are important both in physics and mathematics. At first, we show only in two cases nontrivial solutions exist and they degenerate to solutions of the nonlinear Dirac equation with lower dimension. Next, we show the nonexistence result if the frequency omega is larger than mc^2, and we find nontrivial solutions in L^t, for some t>2, if the frequency equals -mc^2. Last, we introduce a type of holonomic constraints, and give a general method to show the nonexistence of ground states for the constraint system.
主讲人介绍：
郭琪，讲师，中国人民大学。研究方向为临界点理论与变分法，近年来主要研究非线性Dirac方程相关理论、无穷维哈密尔顿系统和辛不变量等问题，目前主持中国博士后科学基金(面上)、国家自然科学基金(青年)。相关研究工作发表在SIAM J. Math. Anal., Calc. Var. Partial Differential Equations, Discrete Contin. Dyn. Syst., J. Math. Phys等国际权威杂志。
