流體力學

The purpose of this one semester course is to introduce to beginning graduate students and senior undergraduate students the elements and basics of the theory of time dependent incompressible Navier Stokes equations, with an aim to prepare our students to participate the joint meeting held by NCTS and MSRI in the summer of 2021. The main reference book which we will used is the well known textbook entitiled “ Lectures on Navier-Stokes Equations” written by the famous mathematician Tai-Peng Tsai, who is one of the top reserchers in the study of the regularity of solutions to the incompressible Navier-Stokes equations. Topics covered in this course would be: Theory of suitable weak solutions to the incompressible Navier-Stokes equation. Serrin criteria regularity, including the recent breakthrough for the L^{infinity}L^3 end-point result. The theory of mild solutions due to the Kato approach. The theory of partial regularity theory. The exclusion of the type I blow up for axi-symmetric Navier-Stokes follow in the 3D setting. (The above topics will be handled by Chi Hin Chan) An introduction to the elements of the theory of incompressible limit (This part will be handed by Dr. Su Cheng Fang with her kind assistance.)

Real Analysis, functional analysis, linear algebra, multi-variable calculus.

Lectures on Navier-Stokes Equations, by Tai-Peng Tsai, Publisher: AMS