Mathematical Foundation of Turbulent Viscous Flows Lectures given at
Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the bl
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C.I.M.E. means Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Center. Conceived in the early fifties, it was born in 1954 and made welcome by the world mathematical community where it remains, in good health and spirit. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities during the past years. So they already know what the C.I.M.E. is all about. For the benefit of future potential users and co-operators the main purposes and the functioning of the Centre may be summarized as follows: Every year, during the summer, Sessions (three or four as a rule) on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. Each Session is generally based on three or four main courses (24–30 hours over a period of 6-8 working days) held from specialists of international renown, plus a certain number of Seminars. A C.I.M.E. Session, therefore, is neither a Symposium, nor a School, but maybe a blend of both. The aim is that of bringing to the attention of younger researchers the origins, later developments, and perspectives of some branch of live mathematics. The topics of the courses are generally of international resonance and the participant of the courses is covering the expertise of different countries and continents. Such combination, gave an excellent opportunity to young participants to be acquainted with the most advanced researches in the topics of the courses and the possibility of an interchange with the world famous specialists. The full immersion atmosphere of the courses and the daily exchange among participants are a first brick in building of international collaboration in Mathematics research. For more information see CIME’s homepage: http://www.cime.unifi.it CIME’s activity is supported by: – Istituto Nationale di Alta Matematica “F.Severi” – Ministero dell’Istruzione, dell’Università e della Ricerca – Ministero degli Affari Esteri - Direzione Generale per la Promozione e la Cooperazione - Ufficio V – Università Franco-Italiana.
Peter Constantin · Giovanni Gallavotti · Alexander V. Kazhikov · Yves Meyer · Seiji Ukai
Mathematical Foundation of Turbulent Viscous Flows Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1–5, 2003 Editors: Marco Cannone, Tetsuro Miyakawa
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Authors and Editors Peter Constantin
Seiji Ukai
Department of Mathematics University of Chicago 5734 University Avenue Chicago, IL 60637, USA e-mail: [email protected]
Department of Applied Mathematics Yokohama National University 79-5 Tokiwadai, Hodogaya Yokohama 240-8501 Japan e-mail: [email protected]
Giovanni Gallavotti Dipartimento di Fisica Università di Roma “La Sapienza” P.le Moro 2, 00185 Roma, Italia e-mail: [email protected]
Marco Cannone Laboratoire d’Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée 5, boulevard Descartes Champs-sur-Marne 77454 Marne-la-Vallée cedex 2 France e-mail: ma
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