Seminar| Institute of Mathematical Sciences
Time: Wednesday, June 10th, 2026,15:00-16:00
Location: IMS, R408
Speaker: Shijun Liao, Shanghai JiaoTong University（廖世俊 上海交通大学）
Abstract:We give a mathematical proof about the spatial symmetry invariance theorem of the Navier-Stokes (NS) turbulence (i.e. turbulent flows governed by NS equations): the exact solution of NS equations under periodic boundary condition maintains the same spatial symmetry as its initial condition forever. This theorem provides an absolute scale to check the accuracy and correctness of NS turbulence. It is found that CNS (clean numerical simulation) results can maintain the same spatial symmetry as initial condition in the whole time interval of simulation, but the corresponding DNS (direct numerical simulation) results quickly lose the spatial symmetry, which clearly indicates that DNS results are badly polluted by numerical noises that are stochastic in space. In other words, DNS violates the spatial symmetry invariance theorem, but CNS complies with it well. Some discussions such as the solution non-uniqueness and ultra-chaotic property of NS turbulence are given.
演讲人介绍：廖世俊是上海交大讲席教授，“海洋工程全国重点实验室”主任，上海市力学学会理事长，JFM副主编。他1992年原创性提出求解强非线性问题的“同伦分析方法”（homotopy analysis method），克服了传统方法依赖物理小参数、解时常发散之局限性，为强非线性问题提供了一个全新的、灵活而通用的解析近似方法。他2009年原创性提出求解混沌系统的“洁净数值模拟”(Clean Numerical Simulation, CNS)，为混沌系统和湍流提供了首个可靠的长时域模拟工具。他撰写了三本英文专著，其论著被SCI检索他引14110次，曾荣获“国家自然科学二等奖”（独立完成人）、“上海市自然科学牡丹奖”、“上海市科技精英”称号，2023年获英国普利茅斯大学荣誉博士学位。