Abstract: It is widely acknowledged that physical laws governing large chaotic systems are primarily revealed through statistically. Our focus centers on temporal and spatial approximations of stationary statistical properties exhibited by dissipative chaotic dynamical systems. We aim to illustrate that suitable temporal/spatial discretization, when regarded as a discrete dynamical system, can asymptotically capture the stationary statistical properties of the continuous dynamical system, provided that it fulfills specific Lax-type criteria.

Moreover, we present a comprehensive framework to elucidate scenarios where the long-term statistics of the system can be effectively approximated using BDF2-based schemes. Our forthcoming discussion will include applications of this framework to the infinite Prandtl number model for convection, along with an exploration of its applicability to the two-dimensional barotropic quasi-geostrophic equations.

Bio-Sketch: Professor Wang obtained his BS and MS degrees from Fudan University, followed by a Ph.D. from Indiana University - Bloomington. He currently serves as the Havener Endowed Chair at Missouri University of Science and Technology and holds the position of Chair Professor at Southern University of Science and technology (on leave). Prior to his current roles, Professor Wang held tenured positions at Fudan University, Florida State University, and Iowa State University.

Prof. Wang's ongoing research concentrates on modern applied mathematics, specifically focusing on areas such as fluid dynamics, groundwater research, geophysical fluid dynamics and turbulence, and big data and machine learning. He employs tools derived from Partial Differential Equations, Dynamical Systems, Stochastic Analysis, Numerical Analysis, and Scientific Computing in his research endeavors. A distinctive hallmark of his work lies in integrating rigorous mathematical techniques with genuine physical applications.

Tencent Meeting: https://meeting.tencent.com/dm/iQkSmfGhpajh                                                                                                                                         ID: 290-437-765        Password: 031212