标题：Singular kinetic McKean-Vlasov SDEs
报告时间：2024年11月4日（星期一）15：30-16：30
报告地点：线上腾讯会议（会议ID：513-157-445）
主讲人：郝子墨
主办单位：数学与统计学院
报告内容简介：
In this talk, we delve into mean-field kinetic stochastic differential equations (SDEs) featuring Gaussian environment noise and singular interaction kernels driven by Brownian motion and α-stable processes. First, we develop paracontrolled calculus within the kinetic framework when the driving noise is Brownian motion. Applying this, we establish global well-posedness for nonlinear singular kinetic equations with both singular environment noise and bounded interaction kernel, contingent upon the well-definition of the products of singular terms. We obtain how such products can be defined in scenarioses where the singular term is a Gaussian random field. Second, when the driving noise takes an α-stable process, we give the well-posedness and provide quantitative estimates for the propagation of chaos related to the kinetic SDEs endowed with singular interaction kernels, such as the Coulomb potential, and devoid of environment noise (The talk is based on joint works with Jean-Francois Jabir, Stephane Menozzi, Michael R¨ockner, Xicheng Zhang, Rongchan Zhu and Xiangchan Zhu).
主讲人简介：
郝子墨于2023年博士毕业于武汉大学数学与统计学院和Bielefeld大学数学学院。现为Bielefeld大学博士后研究员。主要研究方向为奇异系数的SDE。已在 J. Math. Pures Appl., SIAM J. Math. Anal., Bernoulli等国际权威期刊发表多篇学术论文。
