The imagination is struck by the substantial conceptual identity between
the problems met in the theoretical study of physical phenomena. It is
absolutely unexpected and surprising, whether one studies equilibrium
statistical me- chanics, or quantum field theory, or solid state
physics, or celestial mechanics, harmonic analysis, elasticity, general
relativity or fluid mechanics and chaos in turbulence. So when in 1988 I
was made chair of Fluid Mechanics at the Universita La Sapienza, not out
of recognition of work I did on the subject (there was none) but,
rather, to avoid my teaching mechanics, from which I could have a strong
cultural influence on mathematical physics in Rome, I was not
excessively worried, although I was clearly in the wrong place. The
subject is wide, hence in the last decade I could do nothing else but go
through books and libraries looking for something that was within the
range of the methods and experiences of my past work. The first great
surprise was to realize that the mathematical theory of fluids is in an
even more primitive state than I was aware of. Nevertheless it still
seems to me that a detailed analysis of the mathematical problems is
essential for anyone who wishes to do research into fluids. Therefore, I
dedicated (Chap. 3) all the space necessary to a complete exposition of
the theories of Leray, of Scheffer and of Caffarelli, Kohn and
Nirenberg, taken directly from the original works.