报告人：曾小雨

时间：11月14日下午2点

腾讯会议：177-197-251

题目：GNS-inequalities and ground states of relativistic Hartree-Fock model

摘要：In this talk, we present a rigorous mathematical analysis of the relativistic Hartree-Fock model for finite Fermi systems. We first establish an optimal Gagliardo-Nirenberg-Sobolev (GNS) inequality with Hartree-type nonlinearities for orthonormal systems and characterize the qualitative properties of its optimizers. Furthermore, we derive a finite-rank Lieb-Thirring inequality involving convolution terms and show that it is the duality of the GNS-inequality.  For the relativistic Hartree-Fock model,  we prove that ground states exist if and only if the coupling parameter $K<K_\infty^{(N)}$, where $K_\infty^{(N)}$ is the optimal constant in the GNS-inequality. Finally, under suitable assumptions on the external potentials, we calculate the precisely asymptotic behavior of ground states as $K\nearrow K_\infty^{(N)}$. This is based on a joint work with Dr. Yuanda Wu and Pro. Yimin Zhang.

报告人简介：曾小雨，武汉理工大学数学科学研究中心教授，主要从事与薛定谔方程相关的变分问题、抛物方程爆破解构造等研究。主持国家自然科学基金优青、面上项目和青年科学基金项目，并作为核心成员参与国家自然科学基金重点项目。主要成果发表在Trans.AMS、JMPA、JFA、Ann. Inst. H. Poincar'eAnal. Non Lin'eaire等国际期刊上。