报告题目：Approximating long-time statistical properties of complex dynamical systems

报 告 人：王晓明教授（南方科技大学）

报告时间：2023年5月30日  10:00

报告地点：腾讯会议（165143553）

报告摘要：

It is well-known that physical laws for large chaotic systems are revealed statistically. We consider temporal and spatial approximations of stationary statistical properties of disspative chaotic dynamical systems. We demonstrate that appropriate temporal/spatial discretization viewed as discrete dynamical system is able to capture asymptotically the stationary statistical properties of the underlying contimnous dynamical system provided that appropriate Lax type criteria are satisfied. We also show a general framework on when the long-time statistics of the system can be well-approximated by BDF2 based schemes. Application to the infinite Prandtl number model for convection as well as the two-dimensional barotropic quasi-geostrophic equations will be discussed.

报告人简介：

Prof. Wang received his Ph D. in Applied Mathematics from Indiana University - Bloomington in 1996. He was a postdoctoral fellow/Courant Instructor at the Courant Institute before he joined Iowa State University in 1998 where he was promoted to Associate Professor with Tenure in 2001. He moved to Florida State University in 2003 where he was promoted to Tenured Professor and served as the Chair of the Math Department at Florida State University before he retumed to his motherland in 2017. He is curently a Chair Professor of Mathematics at Southem University of Science and Technology and Missouri University of Science and Technology.

Prof. Wang's curent research focuses on modern applied mathematics, especially problems related to fluid dynamics, groundwater research, geophysical fluid dynamics and turbulence, and big data and machine learning He develops and utilizes tools from Partial Differential Equations, Dynanical Systems, Stochastic Analysis, Numerical Analysis and Scientific Computing in his research. A distinctive feature of his work is the combination of rigorous mathematics with genuine physical applications.