hard.wisdom wrote:
>
>
>
> Dear members
>
> is there a rather elementary book
> on Navier-Stokes equation (e.i. fluid dynamics)
> within the framework of harmonic analysis?
>
> best regards,
> anthony

My impression is that most of the books try hard not to be elementary.
The authors like to state the results in maximally general form, and
most general domains, etc, etc.

An elementary book that I liked was:
Doering, Charles R.; Gibbon, J. D. Applied analysis of the Navier-Stokes
equations. Cambridge Texts in Applied Mathematics. Cambridge University
Press, Cambridge, 1995.
The proofs are not necessarily the sharpest, but it is very easy going.
This was the book from which I learned the subject.

If you want something from the point of view of fixed point theorems on
Besov spaces, etc, there is an out of print book, written in French, by
Cannone. I must admit that I haven't read the book, but I went to a
lecture series he gave, and it was remarkably clear. (If you want the
less elementary treatment, there is the book by Lemarie-Rieusset.)

Finally, I am partial to my own paper:
http://www.math.missouri.edu/~stephen/preprints/thin.html
which I think gives an elementary exposition, but more from the approach
described in the Doering-Gibbon book.

Stephen