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.

The only textbook dealing with the mathematical physics in fluid mechanics Includes supplementary material: sn.pub/extras

Autorentext

Giovanni Gallavotti, emeritus, has been fellow at IHES (Paris, 1966-1968) with David Ruelle and post doc at Rockefeller University (New York, 1968-1970) with Mark Kac. He has been, since 1972, full professor in various universities (Napoli, Roma2 and Roma1). He has been long term visitor at IHES, IAS, Nijmegen, Princeton and Rutgers University. His primary research focused subsequently on theoretical and historical aspects of Equilibrium Statistical Mechanics, Quantum field theory, Low temperature Fermi systems, Nonequilibrium and, currently, concentrates on mathematical problems on Fluid mechanics. Recipient of several awards and prizes (Presidente della Repubblica prize, Boltzmann medal, Henri Poincare' prize).

Klappentext
This monograph on fluid mechanics is not only a superb and unique textbook but also an impressive piece of research. The author writes from the vantage point of a mathematical physicist: Having in mind the important applications and approximation techniques used in physics and engineering, he carefully analyses the power of the theory. He examines, among others, the theories of Leray, Ruelle and Takens, and discusses Lorenz's ideas of attractors. This is the only textbook that fully covers turbulence, all the way from the works of Kolmogorov to modern dynamics. This 2nd corrected printing has been thoroughly revised with many changes to improve readability.

Inhalt
1 Continua and Generalities About Their Equations.- 2 Empirical Algorithms.- 3 Analytical Theories and Mathematical Aspects.- 4 Incipient Turbulence and Chaos.- 5 Ordering Chaos.- 6 Developed Turbulence.- 7 Statistical Properties of Turbulence.- Name Index.- Citations Index.