Navier-Stokes Equations and Turbulence - Foias, C.

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Résumé :
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.

Biographie:
Ciprian Foias is an Emeritus Professor in the Department of Mathematics at Indiana University at Bloomington and Professor of Mathematics at Texas A & M University at College Station. He has held numerous visiting professorships, including those at Virje University (Netherlands), Israel Institute of Technology, University of California at San Diego, Université Paris-Sud, and the Collège de France. In 1995, he was awarded the Norbert Wiener prize by the American Mathematical Society. Oscar P. Manley works as a consultant and independent researcher on the foundations of turbulent flows. He has acted as head of the U.S. Department of Energy's Engineering Research Program and as the Program Manager for the Department of Energy's research on magnetic fusion theory. Dr. Manley has held visiting professorships at the Université Paris-Sud and Indiana University. Ricardo Rosa is a Professor of Mathematics at the Universidade Federal do Rio de Janeiro. He has also held positions as Visiting Researcher at the Institute for Scientific Computing and Applied Mathematics at Indiana University and as Visiting Professor at the Université Paris-Sud in Orsay, France. Roger Temam is a Professor of Mathematics at the Université Paris-Sud and Senior Scientist at the Institute for Scientific Computing and Applied Mathematics at Indiana University. He has been awarded an Honorary Professorship at Fudan University (Shanghai), the French Academy of Sciences Grand Prix Alexandre Joannidès, and the Seymour Cray Prize in Numerical Simulation. Professor Temam has authored or coauthored nine books and published more than 260 articles in international refereed journals. His current research interests in fluid mechanics are in the areas of control of turbulence, boundary layer theory, and geophysical fluid dynamics.

Sommaire:
["Introduction and overview of turbulence","Elements of the mathematical theory of the navier-strokes equations","Finite dimensionality of flows","Stationary statistical solutions of the navier-stokes equations, time averages, and attractors","Time-dependant statistical solutions of the navier-stokes equations and fully developed turbulence"]