主讲人：陈丽 德国曼海姆大学讲座教授
时间：2025年6月27日10：00
地点：三号楼332室
举办单位：数理学院
主讲人介绍：陈丽，教授，2001年吉林大学取得博士学位，2003至2013在清华大学任教，2014年至今德国曼海姆大学讲座教授。研究方向是偏微分方程及应用，具体研究兴趣集中在反应扩散及交叉扩散方程组，多粒子系统的平均场极限及动力学模型，量子力学中的物质稳定性问题等。在《Comm. Partial Differential Equations》《SIAM J. Math. Anal.》《J. Stat. Phys.Phys.》《J. Differential Equations》等杂志发表SCI收录学术论文80余篇。曾被应邀到美国、加拿大、法国、意大利、奥地利等国家参加学术会议并做学术报告20余次。
内容介绍：In this talk I will focus on the derivation of effective descriptions for interacting many-body systems, which is an important branch of applied mathematics. We prove a propagation of chaos result for a system of N particles subject to Newtonian time evolution with or without additional white noise influencing the velocities of the particles. We assume that the particles interact according to a regularized Coulomb-interaction with a regularization parameter that vanishes in the N\to\infty limit. The respective effective description is the so called Vlasov-Poisson-Fokker-Planck (VPFP), respectively the Vlasov-Poisson (VP) equation in the case of no or sub-dominant white noise. To obtain our result we combine the relative entropy method from Jabin and Wang (2016) with the control on the difference between the trajectories of the true and the effective description provided in Huang, Liu, and Pickl (2020 for the VPFP case respectively in Lazarovic and Pickl for the VP case. This allows us to prove strong L^1 convergence of the marginals. This talk is based on the joint work with Jinwook Jung, Peter Pickl, and Zhenfu Wang.
