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Foundations of Fluid Dynamics

  • Textbook
  • © 2002

Overview

Authors:
  1. Giovanni Gallavotti

    1. Dipartimento di Fisica, I.N.F.N., Università degli Studi di Roma “La Sapienza”, Roma, Italy

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

Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Continua and Generalities About Their Equations

    • Giovanni Gallavotti
    Pages 1-82

  3. Empirical Algorithms

    • Giovanni Gallavotti
    Pages 83-142

  4. Analytical Theories and Mathematical Aspects

    • Giovanni Gallavotti
    Pages 143-226

  5. Incipient Turbulence and Chaos

    • Giovanni Gallavotti
    Pages 227-286

  6. Ordering Chaos

    • Giovanni Gallavotti
    Pages 287-401

  7. Developed Turbulence

    • Giovanni Gallavotti
    Pages 403-439

  8. Statistical Properties of Turbulence

    • Giovanni Gallavotti
    Pages 441-490

  9. Back Matter

    Pages 491-514
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Keywords

About this book

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.

Reviews

"Gallavotti’s remarkable new book, Foundations of Fluid Dynamics, takes a fresh look at the essential formulation and phenomenology of fluid dynamics as reflected in the research of the 70s, 80s and 90s. [...] Foundations of Fluid Dynamics is strongly recommended, by this reviewer, for acquisition by academic libraries and for the use of anyone with a serious interest in the mathematical foundations of fluid dynamics." (J.H. Lienhard, Applied Mechanics Review, 55/4, 2002)

"This is an advanced textbook suitable for higher level graduate coursework and as a research reference work. [...] All in all, this book presents a broad range of topics in sufficient depth to make it relatively self-contained." (Mathematical Reviews 2003e)

Authors and Affiliations

  • Dipartimento di Fisica, I.N.F.N., Università degli Studi di Roma “La Sapienza”, Roma, Italy

    Giovanni Gallavotti

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