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A Mathematical Introduction to Fluid Mechanics
Alexandre Chorin
Department of Mathematics University of California, Berkeley Berkeley, California 94720-3840, USA

Jerrold E. Marsden
Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, California 91125, USA

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A Mathematical Introduction to Fluid Mechanics

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Libraryof Congress Cataloging in Publication Data Chorin, Alexandre A Mathematical Introduction to Fluid Mechanics, Third Edition

(Texts in Applied Mathematics) Bibliography: in frontmatter Includes. 1. Fluid dynamics (Mathematics) 2. Dynamics (Mathematics) I. Marsden, Jerrold E. II. Title. III. Series. ISBN 0-387 97300-1 American Mathematics Society (MOS) Subject Classification (1980): 76-01, 76C05,76D05, 76N05, 76N15 Copyright 1992 by Springer-Verlag Publishing Company, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer-Verlag Publishing Company, Inc., 175 Fifth Avenue, NewYork, N.Y. 10010. Typesetting and illustrations prepared by June Meyermann, Gregory Kubota, and Wendy McKay The cover illustration shows a computer simulation of a shock diffraction by a pair of cylinders, by John Bell, Phillip Colella, William Crutchfield, Richard Pember, and Michael Welcome.

The corrected fourth printing, April 2000.

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Preface

This book isbased on a one-term course in fluid mechanics originally taught in the Department of Mathematics of the University of California, Berkeley, during the spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approximation procedures. The goals were: • to present some of the basic ideas of fluid mechanics in amathematically attractive manner (which does not mean “fully rigorous”); • to present the physical background and motivation for some constructions that have been used in recent mathematical and numerical work on the Navier–Stokes equations and on hyperbolic systems; and • to interest some of the students in this beautiful and difficult subject. This third edition has incorporated a number of updatesand revisions, but the spirit and scope of the original book are unaltered. The book is divided into three chapters. The first chapter contains an elementary derivation of the equations; the concept of vorticity is introduced at an early stage. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets andrandom walks is presented. The third chapter contains an analysis of one-dimensional gas flow from a mildly modern point of view. Weak solutions, Riemann problems, Glimm’s scheme, and combustion waves are discussed. The style is informal and no attempt is made to hide the authors’ biases and personal interests. Moreover, references are limited and are by no

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Preface

means exhaustive. Welist below some general references that have been useful for us and some that contain fairly extensive bibliographies. References relevant to specific points are made directly in the text.
R. Abraham, J. E. Marsden, and T. S. Ratiu [1988] Manifolds, Tensor Analysis and Applications, Springer-Verlag: Applied Mathematical Sciences Series, Volume 75. G. K. Batchelor [1967] An Introduction to FluidDynamics, Cambridge Univ. Press. G. Birkhoff [1960] Hydrodynamics, a Study in Logic, Fact and Similitude, Princeton Univ. Press. A. J. Chorin [1976] Lectures on Turbulence Theory, Publish or Perish. A. J. Chorin [1989] Computational Fluid Mechanics, Academic Press, New York. A. J. Chorin [1994] Vorticity and Turbulence, Applied Mathematical Sciences, 103, Springer-Verlag. R. Courant and K. O....