流體力學

The goal of this course is to establish the theory of weak solutions to the Stationary Navier-Stokes equation in the setting of Euclidean space. We will first give a comprehensive treatment of the theory of Sobolev space. Then, we will solve the div equation and discuss elliptic regularity estimate for the Stokes equation. With all these preprations, we will disucss basic results about solutions to the stationary Navier-Stokes equation. If time will permit, we will also discuss the theory of time-dependent Navier-Stokes equation.

A student taking this course should have a solid working knowledge in undergraduate analysis, multi-variable calculus and linear algebra. Some knowledge of real and functional analysis is preferred but not absolutely required.

Homework (20% ) Attendance(30%) Oral and written report(40%) Take Home Final Test (10%)

An introduction to the Mathematical Theory of the Navier-Stokes Equations (Steady-State Problems ), by G.P. Galdi, Second Edition, Published by Springer