Seminar on Nonlinear Partial Differential Equations
When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature math
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2 Editors
S.S. Chern 1. Kaplansky c.c. Moore 1.M. Singer
Mathematical Sciences Research Institute Publications
Volume 1
D. Freed and K. Uhlenbeck: Instantons and FourManifolds
Volume 2
S.S. Chern (ed.): Seminar on Nonlinear Partial Differential Equations
Forthcoming
J.
Lepowsky, G. Mandelstam, and I.M. Singer (eds.): Vertex Theory in Mathematics and Physics
S.S. Chern and P. Griffiths: Essays on Exterior Differential Systems
Seminar on N onlinear Partial Differential Equations Edited by s.s. Chern
With 35 Illustrations
Springer Science+Business Media, LLC
S.S. Chem Department of Mathematics University of California Berkeley, CA 94720 U.S.A.
Mathematical Sciences Research Institute 2223 Fulton Street, Room 603 Berkeley, CA 94720 U.S.A.
AMS Subject Classification: 35-02, 35AXX, 35BXX, 35QXX, 73C50, 76-XX
Library of Congress Cataloging in Publication Data Main entry under title: Seminar on nonlinear partial differential equations. (Mathematical Sciences Research Institute publications; 2) Includes bibliographies. 1. Differential equations, Partial-Addresses, essays, lectures. 2. Differential equations, Nonlinear-Addresses, essays, lectures. 1. Chem, Chiing-S hen. II. Series. QA377.S45 1984 515.3'53 84-20210 The Mathematical Sciences Researeh Institute wishes to acknowledge support from the National Science Foundation. © 1984 by Springer Science+Business Media New York Originally published by Springer-Verlag New York Tne. in 1984 Softcover reprint ofthe hardcover Ist edition 1984 AII rights reserved. No part of this book may be translated or reproduecd in any form without written permission from Springer Scienee+Business Media, LLC,
9 8 765 4 3 2 1 ISBN 978-1-4612-7013-3 ISBN 978-1-4612-1110-5 (eBook) DOI 10.1007/978-1-4612-1110-5
Foreword
When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations".
A seminar was organized whose audience
consisted
students
of
graduate
of
the
University
mathematicians who are not experts in the field. 18 of these lectures.
and
mature
This volume contains
An effort is made to have an adequate
Bibliography for further information.
The Editor wishes to take this
opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor
Table of Contents
1
Geometrical and Analytical Questions in Nonlinear Elasticity
Stuart S. Antman
An Introduction to Euler's Equations for an Incompressible Fluid
Alexandre J. Chorin
31
Linearizing Flows and a Cohomology Interpretation of Lax Equations
Phillip Griffiths
37
The Ricci Curvature Equation
Richard Hamilton
47
A Walk Through Partial Differential Equations
Fritz John
73
Remarks on Zero Viscosity Limit for Nonstationary Navier-Stokes Flows with Boundary
Tosio Kato
85
Free Boundary Problems in Mechanics
Joseph B. Keller
99
The Method of Partial Regularity as Applied to the Navier-Stokes Equations
Robert V. Kohn
117
Shock Waves. Incre
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