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I am not entirely sure if I should ask this question here or not, but here goes: can anyone suggest any reference (book, article, etc.) about the Navier-Stokes equations from a mathematical point view? In other words, works that go into detail about the properties of the NS equations as a set of PDE's and the properties of the solutions (if any)(including attempts to prove that the solution is smooth and its energy is bounded over time). I am also interested in alternative models like Leray's, Holm's and Ladyzenskaja's models.

I don't know where to start my search, so any nudge in the right direction is appreciated.

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  • $\begingroup$ Schlichting's book "Boundary-Layer Theory" is more of an advanced engineering text, but it does have a chapter on the NS equations & another on exact solutions. $\endgroup$ – D. Halsey Apr 25 '19 at 18:29
  • $\begingroup$ @D.Halsey Thank you for you suggestion. I am well aware of Schlichting's book, to which i often turn for reference, but I am not looking for specific solutions to simple configurations. I am looking for texts that tackle the NS equations as a mathematical problem. $\endgroup$ – György von Fesz Apr 28 '19 at 12:45
  • $\begingroup$ This is only an article to get a general gimps into a new approach of how energy might be bounded. quantamagazine.org/… Leray's, Holm's models will be waste of time to digest information from. They don't get brought up often, but Ladyzenskaja's model would be a good start. Properties of the NSE can be seen here: terrytao.wordpress.com/2018/09/03/… Good luck :) $\endgroup$ – MrFlu14 Dec 4 '19 at 16:37

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