I am currently working on a PhD project (1st year) involving the Euler equations. I would like to have a strong background on this, especially from the mathematical theory points of view. (since I found that many books written in this topic focus much on the numerical points of view). Also, I found some very good books on the Navier-Stoke equation, but is there any specific literature focusing only on Euler equation? Briefly, I need a book that:
- explain the derivation of Euler equation. (from physical points of view)
- explain the roles of each terms in the equation.
- explain the mathematical theory developed on it. (analyze the existence and uniqueness of solution, well-posed, convergence of approximation solution (by numerical methods), limitation of today's knowledge on solving it, ...)
- some parts about numerical experiments (with analysis and explanation). Thank you for all of your recommendation.