Topics in PDE: Navier-Stokes Equations

I am interested in learning about the Navier-Stokes equation. I recently came across a very nice book
``The Three Dimensional Navier-Stokes Equation''
by James Robinson, Jose Rodrigo and Witold Sadowski.
I am seeking an audience that is willing to hear me lecture on whatever I have managed to understand from the first four chapters of that book (I haven't attempted anything beyond that.......trying to understand the first four chapters is a sufficiently ambitious goal).
My goal is to try to unravel the proof of the existence of a weak solution for the Navier-Stokes equation.
If you are interested in listening to what I have figured out, then you can drop me an email. I will add you to a mailing list.   I will try to schedule the lecture(s) at a time convenient for you.

My email address is ritiwm [at] niser.ac.in

A knowledge of Measure Theory, L^p spaces, Distributions and  Sobolev Spaces will be helpful (although I will review these concepts).
To give you an idea about the book, the chapters are organized as follows:
Chapter (0): Derivation of Navier Stokes Equation I plan to skip this for now

Chapter (1): An excellent summary of all the spaces and corresponding Theorems that you would have studied in a Measure Theory course and then in a PDE course. It is an excellent chapter to refresh your knowledge about L^p spaces and Sobolev spaces.

Chapter (2): Focuses on the Helmholtz-Weyl decomposition and introduces the all important Stokes operator.
Chapter (3): Weak formulation of Navier Stokes equation.
Chapter (4): Proof of the existence of Weak solution.

My plan is to do a top down approach, namely I want to start from Chapters 3 and 4 and then work my way down to what I need (which will be mainly Chapters 1 and 2). Initially, I will try to give ''proofs'' modulo N statements. The hope is that as time progresses, N will get smaller.

Google Sites

Report abuse

Page details

Page updated

Google Sites

Report abuse