This book aims to bridge the gap between practicing mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists as well as the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors, who analyze turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments.
The mathematical technicalities are kept to a minimum within the book, enabling the discussion to be understood by a broad audience. Each chapter is accompanied by appendices that give full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers, and physicists.