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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.
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  • $\begingroup$ Well, concerning your first point, Galdi's "An introduction to the mathematical theory of the Navier-Stokes equations" could be a good start (if you're comfortable with the basics of real analysis). Temam's books (there are at least three I know of) are, I believe, a standard reference. Besides these most is in article form I believe, or in texts on fluid dynamics (maybe you could look into these for your other points). $\endgroup$
    – Jose27
    Commented Apr 28, 2011 at 4:52
  • $\begingroup$ In terms of motivation, and as mentioned by Jose27, any introductory text on fluid dynamics will suffice. $\endgroup$
    – picakhu
    Commented Apr 28, 2011 at 5:38
  • $\begingroup$ If you're looking for a very physical point of view, try Acheson's "Elementary Fluid Dynamics" (Oxford Univ. Press). $\endgroup$
    – Gerben
    Commented Apr 28, 2011 at 6:36

2 Answers 2

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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.

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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

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