一、题目

Approximation of long time statistical properties of large dissipative chaotic dynamical systems

二、主讲人

王晓明

三、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 dissipative 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 continuous dynamical system provided that two conditions are satisfied:

（i）The discrete dynamical system inherits the dissipativity of the original system uniformly (with respect to time step and spatial grid size) in some appropriate sense;

（ii）The discrete dynamical system converges uniformly on the unit time interval [0; 1] to the original system uniformly for initial data coming from the union of the global attractors.

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.

四、主讲人简介

王晓明教授本科和硕士毕业于复旦大学，博士毕业于印第安纳大学布卢明顿分校，在纽约大学库朗研究所接受博后训练。现任南方科技大学讲席教授、数学系系主任、深圳国家应用数学中心执行主任，国家级高层次特聘专家，曾任复旦大学特聘教授，美国佛罗里达州立大学终身正教授及数学系主任，具有30多年在美国和中国知名研究型大学科研教学的经验，在应用与计算数学，特别是在与流体力学、地球物理流体力学、地下水研究和材料力学当中的数学问题的研究方面有深入的结果，由剑桥大学出版社出版专著一本，在重要国际期刊如CPAM等杂志发表论文90余篇。

五、邀请人

芮洪兴 数学学院教授

六、时间

10月23日（周六）10:00

七、地点

中心校区知新楼B座924报告厅

八、主办方

山东大学数学学院