Review of the hardback: 'The authors are distinguished researchers who have made fundamental contributions to mathematical fluid dynamics over their careers. The aim of the volume is, in the authors' own words, 'to let physicists and engineers know about existing mathematical tools from which they might benefit [and] … to help mathematicians learn what physical turbulence is about so they can focus their research on problems of interest of physics. …' The monograph is a substantial step toward bringing together physicists' and engineers' theoretical treatments of turbulence with mathematicisns' rigorous analysis of the Navier-Strokes equations and their solutions. In this regard the book is the first of its type. This book is far from elementary, but the authors' efforts to make it accessible on several levels make it a valuable and unique resource for researchers interested in both turbulence theory and mathematical analysis. I hope, as do the authors, that this work will help to establish new and constructive lines of communication between these two communities.' SIAM Review

• Preface; Acknowledgements; 1. Introduction and overview of turbulence; 2. Elements of the mathematical theory of the Navier–Stokes equations; 3. Finite dimensionality of flows; 4. Stationary statistical solutions of the Navier–Stokes equations, time averages and attractors; 5. Time-dependent statistical solutions of the Navier–Stokes equations and fully developed turbulence; References; Index.

Review of the hardback: 'The authors are distinguished researchers who have made fundamental contributions to mathematical fluid dynamics over their careers. The aim of the volume is, in the authors' own words, 'to let physicists and engineers know about existing mathematical tools from which they might benefit [and] … to help mathematicians learn what physical turbulence is about so they can focus their research on problems of interest of physics. …' The monograph is a substantial step toward bringing together physicists' and engineers' theoretical treatments of turbulence with mathematicisns' rigorous analysis of the Navier-Strokes equations and their solutions. In this regard the book is the first of its type. This book is far from elementary, but the authors' efforts to make it accessible on several levels make it a valuable and unique resource for researchers interested in both turbulence theory and mathematical analysis. I hope, as do the authors, that this work will help to establish new and constructive lines of communication between these two communities.' SIAM Review

• Preface; Acknowledgements; 1. Introduction and overview of turbulence; 2. Elements of the mathematical theory of the Navier–Stokes equations; 3. Finite dimensionality of flows; 4. Stationary statistical solutions of the Navier–Stokes equations, time averages and attractors; 5. Time-dependent statistical solutions of the Navier–Stokes equations and fully developed turbulence; References; Index.

Review of the hardback: 'The authors are distinguished researchers who have made fundamental contributions to mathematical fluid dynamics over their careers. The aim of the volume is, in the authors' own words, 'to let physicists and engineers know about existing mathematical tools from which they might benefit [and] … to help mathematicians learn what physical turbulence is about so they can focus their research on problems of interest of physics. …' The monograph is a substantial step toward bringing together physicists' and engineers' theoretical treatments of turbulence with mathematicisns' rigorous analysis of the Navier-Strokes equations and their solutions. In this regard the book is the first of its type. This book is far from elementary, but the authors' efforts to make it accessible on several levels make it a valuable and unique resource for researchers interested in both turbulence theory and mathematical analysis. I hope, as do the authors, that this work will help to establish new and constructive lines of communication between these two communities.' SIAM Review

• Preface; Acknowledgements; 1. Introduction and overview of turbulence; 2. Elements of the mathematical theory of the Navier–Stokes equations; 3. Finite dimensionality of flows; 4. Stationary statistical solutions of the Navier–Stokes equations, time averages and attractors; 5. Time-dependent statistical solutions of the Navier–Stokes equations and fully developed turbulence; References; Index.