概率统计讨论班——On the compressible Euler equation and the Langevin deformation of flows on Wasserstein space
报告人:李向东,中国科学院系统与数学科学研究院
时间:2025年4月10日,15:30-17:00
地点:海纳苑2幢312室
摘要:In my previous work and my joint work with Songzi Li, we proved the W-entropy formula for the heat equation of the Witten Laplacian on Riemannian manifolds and the W-entropy formula for the Wasseestein geodesic flow on Riemannian manifolds. We introduced the Langevin deformation of flows, which is a natural interpolation between the gradient flow of the Boltzmann entropy and the Wasserstein geodesic flow and is closely related to the compressible Euler equation with damping on manifolds. We proved the existence and uniqueness of the compressible Euler equation with damping on manifolds, the W-entropy formula for the Langevin deformation of flows and its convergence when the viscosity coefficient tends to zero and to infinity respectively. In recent works with Songzi Li, Rong Lei and Yuzhao Wang, we further extend our results to the compressible $L^p$-Euler equation with damping and the $L^p$-Langevin deformation of flows on over Riemannian manifolds. Our results are new even for the one dimensional Euler equations with dampings. I will give a survey on these works.
报告人简介:李向东,主要研究领域:随机分析、随机微分几何、随机矩阵、最优传输理论。1990年本科毕业于武汉大学,1994-1999年获中国科学院应用数学研究所及葡萄牙里斯本大学博士学位,1999-2003年先后在里斯本大学与牛津大学从事博士后研究,2003年获法国图卢兹大学Maitre de Conference终身职位,2007年获法国图卢兹大学“指导研究证书”(Habilitation a Diriger des Recherches ),2008-2009年任复旦大学数学科学学院教授。2009年至今,先后任中国科学院数学与系统科学研究院研究员、华罗庚应用数学首席研究员。2015年至今,兼任中国科学院大学岗位教授。
联系人:苏中根(suzhonggen@zju.edu.cn)