I am in my second year of master in Mathematics and one of my courses consists of a reading of Navier-Stokes Equations by Roger Temam. We have proven the existence for the weak Stokes and Navier-Stokes (defined on a bounded domain) in a stationary and non-stationary regime using a Galerkin method.
Now I have to do a 2 hours presentation on the subject of my choice (still related to hydrodynamics) and I would like to know if one of you had an idea of something I could talk about. I looked on the internet for an article that could match my critera but all I found was way too advance or too long for what I am looking for. I am looking for a paper that could be presented in two hours, that is accessible to a master student (who has read Temam's book) and that is an important result in the modern understanding of the Navier-Stokes equations (a paper by Leray, Ladyzhenskaya, Fujita-Kato, Lions, … for example). Could one of you, who has a better knowledge of what has been done in hydrodynamics, give me some advice on this subject?
I first asked the question on Stackexchange Mathematics but I don't know which site is best for what I'm looking for. You may find here my question on Stackexchange Mathematics.
Best Answer
Beale Kato Majda criteria: Beale, J. Thomas, Tosio Kato, and Andrew Majda. "Remarks on the breakdown of smooth solutions for the 3-D Euler equations." Communications in Mathematical Physics 94.1 (1984): 61-66.
Provides a necessary condition for blowup, used frequently in modern research on NS (1500+ citations) and is only 6 pages long (!).