Navier-Stokes Equations and Turbulence (Encyclopedia of Mathematics and its Applications, Series Number 83)

This Book Aims To Bridge The Gap Between Practising Mathematicians And The Practitioners Of Turbulence Theory. It Presents The Mathematical Theory Of Turbulence To Engineers And Physicists, And The Physical Theory Of Turbulence To Mathematicians. The Book Is The Result Of Many Years Of Research By The Authors To Analyse 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 Language To Be At A Level Understood By A Broad Audience. Each Chapter Is Accompanied By Appendices Giving Full Details Of The Mathematical Proofs And Subtleties. This Unique Presentation Should Ensure A Volume Of Interest To Mathematicians, Engineers And Physicists. C. Foias ... [et Al.]. Includes Bibliographical References And Index.

This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. It is the result of many years of research by the authors to 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 that had been arrived at earlier by phenomenological arguments. Appendices give full details of the mathematical proofs and subtleties.

Written for mathematicians, physicists, and engineers, this book draws together the perspectives of their various disciplines, explaining both the mathematical and physical theory behind turbulence. Turbulence is analyzed using Sobolex spaces and functional analysis, deriving from the Navier-Stokes equations the conventional theory which had previously only been supported by phenomenological arguments. Each chapter is followed by appendices presenting the full details of the mathematical proofs. This text is the result of many years of research by authors to analyse turbulence using Sobolev spaces and functional analysis. It should ensure a volume of interest to mathematicians, engineers and physicists In this chapter we first briefly recall, in Section 1, the derivation of the Navier-Stokes equations (NSE) starting from the basic conservation principles in mechanics: conservation of mass and momentum.