国际学者教学公告
2012-12-19       培养处

 

不可压缩Navier-Stokes方程系列讲座

 

主讲人:王长友教授(University of Kentucky, USA )

邀请人:保继光教授

 

简介:美国肯塔基(Kentucky)大学的王长友(Wang Changyou)教授将在1218日至31日访问我校数学科学学院。此次访问期间王长友教授将开设关于不可压缩Navier-Stokes方程的系列讲座。欢迎有兴趣的研究生、博士生,以及高年级本科生参加!

 

地点:后主楼1129

时间:下午14:00-17:00

      1219-21日(周三至周五),1224-28日(周一至周五)。

 

联系人:李海刚老师hgli@bnu.edu.cn

 

Outline of the course

The incompressible Navier-Stokes Equation (NSE) is the fundamental equation to describe the motion of the incompressible, viscous fluid from physics. It is used to model the weather, ocean currents, water flow in a pipe and air flow around a wing. Coupled with Maxwell's equation and Fokker-Planck equation, it can be used to study magnetohydrodynamics (MHD) and complex fluid flows including viscoelastic fluids respectively. NSEs are also of great interests from mathematical viewpoints, in which many fundamental questions are yet to be understood.

 

No previous knowledge of these topics will be assumed, but the participants should have some knowledge of Ordinary and Partial Differential Equations, at the level of an introductory graduate course. Open problems of various level of difficulty will be mentioned. Pending on the availability of schedule, each student may be assigned to study and present an article at the end of the mini-course.

 

Within this course, we aim to introduce some of the very basic issues on NSE varying from existence, uniqueness, stability to regularity. In particular, we plan to discuss the following topics:

1、The basic of fluid mechanics: Derivation and basic property of Navier-Stokes equation.

2、Model equations: Simple model equations which are more manageable than the Navier-Stokes equation can bring important insights into these problems and will be discussed at various points.

3、The linear Stokes equation: Basic theory behind both steady and dynamic cases.

4、The steady Navier-Stokes equation:  Existence, regularity, and stability.

5、The dynamic Navier-Stokes equation: Ladyzhenskya's theory in dimension two, Leray and Hopf's theory in dimension three, Serrin-Prodi's regularity and uniqueness theorem, and Caffarelli-Kohn-Nirenberg and Escauriaza-Seregin- Sverak's regularity theories.



返回顶部】【打印本页