Program
Methods of Geometric Analysis in Fluid Mechanics
Student No.:50
Time:Tue/Thu 10:10-12:00
Instructor:Demetrios Christodoulou,Shuang Miao  
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2013-2-26
Ending Date:2013-4-16

Description:

 

 

 

 

The course shall give an outline of the methods of geometric analysis introduced in the monograph “The Formation of Shocks in 3-Dimensional Fluids”. This monograph treated the relativistic Euler equations describing the motion of a perfect fluid with an arbitrary equation of state in the framework of special relativity. A follow up monograph treats the same topic in the classical framework. Theorems are established which cover the maximal classical development, showing in particular that the boundary of its domain has a singular part where the inverse density of the wave fronts vanishes. The theorems give a detailed description of the geometry of the singular boundary and of the behavior of the solutions at this boundary. A complete picture of shock formation is obtained. The central concept on which the approach is based is that of the acoustical spacetime manifold.

 

This course has three parts:

 

Part 1 (first meeting on 2013-2-26) will be taught by Dr. Shuang Miao. The goal of this part is to introduce the geometric backgrounds.

 

Part 2 (from 2013-3-19 to 2013-4-11) will be taught by Prof. Christodoulou. The goal is to outline the method and main structures for the formation of shocks in 3D fluids.

 

Part 3 (first meeting at 2013-4-16) will be taught by Dr. Shuang Miao. The goal is to carry out all the details of the proof.

 

 

Prerequisite:

 

 

 

 

 

Basic real analysis and differential geometry

 

 

 

Reference:

 

 

D. Christodoulou: “The Formation of Shocks in 3-Dimensional Fluids” , EMS Monographs in Mathematics, EMS Publishing House, 2007 (ISBN 978-3-03719-031-9)