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系列课程

Navier-Stokes and Euler Equations, and Certain Geophysical Models

报告人：Prof. Edriss S. Titi （Texas A&M University and The Weizmann Institute of Science）

课程介绍:

In this series of lectures I will be covering two main topics. The first part will be concerning the Navier-Stokes and Euler equations. The second part will discuss the question of global regularity of certain geophysical flows.

The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, which are called the “Primitive Equations”, is often prohibitively expensive computationally, and hard to study analytically. In these introductory lectures, aimed toward graduate students, I will survey the mathematical theory of the 2D and 3D Navier-Stokes and Euler equations, and stress the main obstacles in proving the global regularity for the 3D case, and the computational challenge in their direct numerical simulations. In addition, I will emphasize the issues facing the turbulence community in their turbulence closure models. However, taking advantage of certain geophysical balances and situations, such as geostrophic balance and

the shallowness of the ocean and atmosphere, I will show how geophysicists derive more simplied models which are easier to study analytically. In particular, I will prove the global regularity for the 3D Primitive equations of large scale oceanic and atmospheric dynamics with various kinds of anisotropic viscosity and difusion. Moreover, I will also show that for certain class of initial data the solutions of the inviscid 2D and 3D Primitive Equations blowup (develop a singularity) infinite time. Furthermore, I will present some recent results concerning the regularity of certain tropical atmospheric models with moisture and clouds formation. If time allows I will also discuss some new algorithms for feedback control and data assimilation for the Navier-Stokes equations and otheratmospheric and climate models.

地点：首都师范大学本部教二楼527教室

时间：12月4、5、7号 上午 9:30-11:00

欢迎全体师生积极参加！