Math Question: 2D Euler Equations
 

New to CFD and trying to understand some of the physics behind it. I'm trying to find the solution to the characteristics 2D steady state Euler equations.

If you look at the attached image, I don't understand how to get from 1 to 2. Any advice is much appreciated but please use detail and write it out if possible!

Also, for both supersonic and subsonic are the 2D Euler equations hyperbolic or elliptic? How do you prove it?

Thanks

Have a look to the Zucrow book, also the way to understand the ellipric/hyperbolic character is to introduce the potential function and study the nature (real or not) of the characteristic curves

Gotchya, do you know the exact title of the book?

Zucrow-Hoffman Gas Dynamics Vol.1 and 2

Steady State Euler Equation: It is elliptic for subsonic. Parabolic for M=1 and hyperbolic for supersonic. The proof is based on finding the eigen values of the PDE. The proof is given in most of the CFD books. You can refer CFD by Anderson.