References for the Navier-Stokes equations

Question

For understanding the Navier-Stokes equations, are there any references which may include one or more of the followings:

• mathematical rigorousness
• motivation
• preliminaries
• introduction
• etc.

Answer 1

As this is one of the Clay Institute of Mathematics Millennium Problems, I refer you to their webpage on the problem and to their write-up for the prize. It contains several references about the problem and some of the results on the problem. Their webpage also has a video lecture by Luis Caffarelli on the problem, which I think is really cool.

Answer 2

This[1] is a great textbook on fundamentals of computational fluid dynamics, which includes a derivation of equations.

References:

[1] Hirsch, Charles. (2007). Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics. Elsevier