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I'm a beginning graduate student, and I'm interested in learning more about Fluid Mechanics and, in particular, the Navier stokes Equations. I would like to know: are there are some sort of free survey articles (available online) that discuss the problem? Also, I would like to know if there are any articles that discuss the the possible physical implications of the solutions (assuming it is answered affirmatively).

Thanks, Bharadwaj

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Have you checked the usual suspects? Google Scholar? – Qiaochu Yuan May 28 '10 at 3:45
Why not a book on fluid dynamics if you really want a physical understanding of Navier-Stokes and its solutions? D.J. Acheson's book is a decent introduction. – j.c. May 28 '10 at 13:20
I second jc's comment on Acheson. – Steve Huntsman May 28 '10 at 15:04
Please change to community wiki. thank you – vonjd Oct 26 '10 at 12:52

Terry Tao wrote a blog article a few years ago:

Why global regularity for Navier-Stokes is hard

and another which followed up on some aspects (and links through to an arxiv preprint too): A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation

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If you don't know about it, this is one of Clay Math's Millennium Problems, They have a brief review with some citations that may be useful. The website claims there's a video of a lecture on it, too, but I haven't watched it so I do not know how useful it would be.

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See Roger Temam's review.

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I made a link to a book. I hope it was the right one. – S. Carnahan Oct 26 '10 at 12:08
Yes, it is a good book and somehow necessary for researchers of NS-Eq. Temam also has an article name:some developments on Navier-Stokes equations in the second half of 20th century. Although this is written in ten years ago, it is of great value. Anyhow, we did not cover a long distance in these ten years. Another book worth reading is Recent developments in the Navier-Stokes problem (P G Lemarié-Rieusset), using harmonica analysis method. – zqt Oct 28 '10 at 0:17

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