报告摘要：One of the major problems in the study of statistical fluid mechanics is to provide good descriptions of the distributions of fluid dynamics variables. According to Kolmogorov, fluid dynamic variables for a turbulent flow such as velocity, vorticity,pressure and etc. are random fields , whose distributions are very difficult to determine.In this talk I report the recent discovery of the evolution equation for the PDF of the vorticity field, which takes form of parabolic-transport equations of second order, and address some PDE problems which will be interesting in the study of turbulence.