Mathematical Fluid Mechanics Recent Results and Open Questions
Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly surv
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Giovanni P. Galdi School of Engineering Department of Mechanical Engineering University of Pittsburgh 3700 O'Hara Street Pittsburgh, PA 15261 USA e-mail: [email protected]
John G. Heywood Department of Mathematics University of British Columbia Vancouver BC Canada V6T 1Y4 e-mail: [email protected]
Rolf Rannacher Institut fur Angewandte Mathematik Universitat Heidelberg 1m Neuenheimer Feld 293/294 69120 Heidelberg Germany e-mail: [email protected]
Advances in Mathematical Fluid Mechanics is a forum for the publication of high quality monographs, or collections of works, on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. Its mathematical aims and scope are similar to those of the Journal of Mathematical Fluid Mechanics. In particular, mathematical aspects of computational methods and of applications to science and engineering are welcome as an important part of the theory. So also are works in related areas of mathematics that have a direct bearing on fluid mechanics. The monographs and collections of works published here may be written in a more expository style than is usual for research journals, with the intention of reaching a wide audience. Collections of review articles will also be sought from time to time.
Mathematical Fluid Mechanics Recent Results and Open Questions Jif! Neustupa Patrick Penel Editors
Springer Basel AG
Editors' addresses: Jifi Neustupa Department of Technical Mathematics Faculty of Mechanical Engineering Czech Technical University Karlovo nam. 13 121 35 Praha 2 Czech Republic
Patrick Penel Departement de Mathematiques Universite de Toulon et du Var B.P.132 83957 La Garde Cedex France
e-mail: [email protected]
e-mail: [email protected]
2000 Mathematical Subject Classification 76D05, 35Q30; 76M1 0, 76N1 0, 35B32
A CIP catalogue record for this book is available from the library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Mathematical fluid mechanics: recent results and open questions I Jifi Neustupa ; Patrick Penel, ed. - Basel; Boston; Berlin: Birkhauser 2001 (Advances in mathematical fluid mechanics)
ISBN 978-3-0348-9489-0 ISBN 978-3-0348-8243-9 (eBook) DOI 10.1007/978-3-0348-8243-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained.
© 2001 Springer Basel AG Originally published by Birkhauser Verlag in 2001 Softcover reprint of the hardcover 1st edition 2001 Printed on acid-free paper produced from chlorine-free pulp. TCF 00
ISBN 978-3-0348-9489-0 987654321
www.birkhauser-science.com
Contents Foreword ................. .. ................. .. ................. . ...........
VB
Claude Bardos: What Use for the Mathematical Theory of the Navier- S
