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Editors F. John J .E. Marsden L. Sirovich M. Golubitsky W. Jager

Texts in Applied Mathematics

1. SiIrwich: lDtroduction to Applied Matbematial. 2. WiggiM: Iotroduction to Applied Nonlinear Dynamic:aI SyItems and Chaos. 3. HQ/e~ Differenlial Equatiolll: An Iotroduction to Dynamics and BifurcatiollS. 4. Chorin/Manden: A Mathematical Introduction to Fluid MechaDic:s, 2nd cd.

A.J. Chorin

J .E.

Marsden

A Mathematical Introduction to Fluid Mechanics Second Edition

With 86 Illustrations

Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong

A.J. Chorin J .E. Marsden Department of Mathematics University of California Berkeley, CA 94720 USA Editors F.John Courant Institute of Matheinatical Sciences New York University New York, NY 10012 USA

J.E. Marsden Department of Mathematics University of California Berkeley, CA 94720 USA

M. Golubitsky Department of Mathematics University of Houston Houston, TX 77004 USA

W.Jager Department of Applied Mathematics U niversitat Heidelberg 1m Neuenheimer Feld 294 6900 Heidelberg, FRG

L. Sirovich

Division of Applied Mathematics Brown University Providence, RI 02912 USA

Mathematics Subject Classification (1980): 76-01, 76C05, 76D05, 76N05, 76N15 Library of Congress Cataloging-in-Publication Data Chorin, Alexandre Joel. A mathematical introduction to fluid mechanics I Alexandre Chorin, Jerrold Marsden. cm.-(TAM texts in applied mathematics) p. Includes index. ISBN· 13: 978'1'4684'0366-4 1. Fluid mechanics. I. Marsden, Jerrold E.

III. Series. QA90l.C53 532--dc20

II. Title.

1990

90-9823 CIP

Printed on acid-free paper. The first edition was published in the Universitext series, 1979 by Springer-Verlag New York, Inc. © 1990 Springer-Verlag New York Inc. Softcover reprint of the hardcover 2nd edition 1990 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of.information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

Camera-ready copy prepared by the authors.

9 8 7 6 5 4 3 2 1 ISBN· 13: 978'1'4684'0366'4 DOl: 10.10071978-1-4684'0364'0

e-ISBN-13: 978'1'4684'0364-0

Series Preface Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the es