Table Of ContentNonlinear Problems in
Mathematical Physics and
Related Topics I
In Honor of Professor
O. A. Ladyzhenskaya
INTERNATIONAL MATHEMATICAL SERIES
Series Editor: Tamara Rozhkovskaya
Sobolev Institute of Mathematics of the Siberian Branch
of the Russian Academy of Sciences, Novosibirsk, Russia
NONLINEAR PROBLEMS IN MATHEMATICAL PHYSICS AND RELATED
TOPICS I: In Honor of Professor O. A. Ladyzhenskaya
Edited by M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov, N. N. Uraltseva
NONLINEAR PROBLEMS IN MATHEMATICAL PHYSICS AND RELATED
TOPICS II: In Honor of Professor O. A. Ladyzhenskaya
Edited by M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov, N. N. Uraltseva
A Continuation Order Plan is available for this series. A continuation order will bring delivery of
each new volume immediately upon publication. Volumes are billed only upon actual shipment.
For further information please contact the publisher.
Nonlinear Problems in
Mathematical Physics and
Related Topics 1
In Honor of Professor
O. A. Ladyzhenskaya
Edited by
Michael Sh. Birman V sevolod A. Solonnikov
St. Petersburg University Steklov Institute of Mathematics RAS
St. Petersburg, Russia St. Petersburg, Russta
Stefan Hildebrandt Nina N. Uraltseva
University of Bonn St. Petersburg University
Bonn, Germany St. Petersburg, Russia
Springer Science+Business Media, LLC
ISBN 978-1-4613-5234-1 ISBN9 78-1-4615-0777-2 (eBook)
DOI 10.1007/978-1-4615-0777-2
C2002SPIinlter Science+Business Media New YorIr.
Originally publishtil by Klu"fr I Pltnum Publishel'1, New \'ork in 2002
Softcover rcpnnl afthe IIardcoVeT 1$1 edition 2002
hnp:l/www.wkap.nll
1098765432 1
A C.LP. rttord for this book is available from tlx: Library of Congrcss
An rights reserved
No part of this book may Ix: reproduced. stare<! in a retrieval system. or transmined in any
rOmi or by any means. electronic. mecllanical, photocopying. microfilming. rttording. or
otherwise. witlioul written permission rrom Ilie Publisher. witli the exception of any material
supplied specifically for tlx: purpose of being entercd and eXel::Uled on il computer system. for
exclusive use by tlx: purchasc:r of tlie work.
To Olga Aleksandrovna Ladyzhenskaya
with love and admiration
Acknowledgments
of the Series Editor
My deep thanks to all who helped to gather, prepare, and publish the first
two volumes of the series in two languages in a very short time:
Deputy Director of IDMI, Dean of the Math. Dept. of Novosibirsk State
University, Professor Sergei Goncharov for his constant moral and adminis
trative support of all my publishing projects, including this series.
Publishing Director of Kluwer / Plenum Publishers, Ken Derham who
played a crucial role in the appearance of this series and who believed new
fruitful ideas and principles of fast publications based on modern computer
technologies and electronic international communications that were first dis
cussed at our meeting in Moscow on 10 September, 2001 and were realized in
a half year only due to Ken's support.
Henry Gomm (Kluwer / Plenum Publishers) for our very good work in
tandem on preparing the English edition of the volumes.
The Computer Committee of the University of Pennsylvania and, espe
cially, Professor Jerry Kazdan who kindly kept my visitor's account rtama
[email protected] open for working with these volumes, which provided me
with a stable connection with the authors and editors in spite of all problems
with the server "math.nsc.ru."
Co-Director of the Mathematical Genealogy Project, supplied with a nice
site http://mathgenealogy.mnsu.edu, Professor Harry Coonce for his kind
help and also Dr. Darya Apushkinskaya for her assistance in constructing the
mathematical genealogy tree of Professor O. A. Ladyzhenskaya.
The Volume Editors, Professors M. Sh. Birman, S. Hildebrandt, V.
A. Solonnikov, and N. N. Uraltseva who carefully selected invited authors
for these volumes and edited both Russian and English versions and, especially,
Professor V. A. Solonnikov for his all-round support of this project.
All the authors who responded to me and supported this edition by their
excellent new results and who worked hard in order to submit their papers (the
most of which were specially written for this series) in an unusually short time
(1-3 months) and promptly answered any questions or requests.
Tamara Rozhkovskaya
Series Editor and the Russian Publisher of the series
March, 2002, Novosibirsk and London
Vll
Main Topics
The choice of the main topics was motivated by the fields of mathematics in which
the world-known results of Professor O. A. Ladyzhenskaya were of the most influence
and inspired the development of further investigations
I. Navier-Stokes Equations and Other Mathematical Problems
in the Theory of Viscous Fluids
• Compressible and incompressible Navier-Stokes equations
• Mathematical analysis of Navier-Stokes equations in bounded and
unbounded domains
• Existence, uniqueness, and regularity of solutions
• Differentiability properties of solutions
• Stability and long time behavior of solutions, asymptotical analysis
• Properties of solutions in domains with nonsmooth boundaries
• Mathematical models of inviscous fluids and non-Newtonian fluids
II. Nonlinear Partial Differential Equations
• Fully nonlinear PDE's and quasilinear PDE's
• Boundary-value problems for nonlinear elliptic equations and systems
• Initial-boundary-value problems for parabolic equations and systems
• Initial-boundary-value problems for hyperbolic equations and systems
• Existence and uniqueness of weak and classical solutions
• Partial regularity and differentiability properties
• Approximation methods for solving problems of mathematical physics
• Properties of function spaces used in the study of PDE's
• Blow-up theorems for quasilinear hyperbolic equations
• Semigroups generated by initial-boundary-value problems
• Calculus of variations and applications to mathematical physics
III. Mathematical Aspects of Computational Analysis
• Approximation methods
• Convergence of numerical methods
• A priori and a posteriori estimates of the accuracy of approximations
ix
"-
The Mathematics Genealogy Project
http://mathgenealogy.mnsu.edu
This tree only follows a formal information from this site
at the Minnesota State University,where one can find an
information about more than 53 000 mathematicians,
their advisors and former students
But there would be a large garden if we try to mention
all actual learners of Professor O. A. Ladyzhenskaya,
all who entered in Mathematics through her seminars
and lectures, read her books and papers, absorbed
her ideas and continued her results and methods
x
J.Mattes
E.Stern D.Apushkinskaya G.Bizhanova
A.Arkhipova E.Denisova
N.lvochkina I. Erunova
N.Reshetikhin F.Gumbatov A.Nazarov E.Frolova
D.Ugurly T.Rozhkovskaya A. Khachatryan
A. Its
A.Venkov F.Tahamtani K.Pileckas
V.Tarasov S.Merkur'ev M.Polat Sh.Sahaev
L. Dmitrieva L.lskenderov
V.Korepin
M.Skriganov
S.Shatashvili M.Houshiyari
A.Fedotov
F.Smirnov S.lsaeva
E.Grinina
P.Kulish I.Gulec
V.Sukhanov
M.Gasanov
L.Takhtajan
L. Kalitievski Yu.Badalov
A.N.Kiriliov
A.Budylin
A. Bytsko
G.Perel'man
Arefeva
A.Vakulenko
B.Pavlov
A.Alimov
V.Popov
E.Sklyanin
A.Reiman
Olga Aleksandrovna
LADYZHENSKAYA
Magister 1947 PhD 1949
Moscow University
Advisor
xi
List of Contributors I
Giovanni ALESSANDRINI (Trieste, Italy)
Universita di Trieste Via A. Valerio 12/1, 34127 Trieste, Italy
E-mail: [email protected]
Vladimir I. ARNOLD (Moscow, Russia - Paris, France)
V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences,
Gubkina 8, Moscow GSP-l 117966, Russia;
CEREMADE, Universite Paris- Dauphine, PI. du Marechal de Lattre
de Tassigny, 75775 Paris, France
E-mail: [email protected]@ceremade.dauphine.fr
J. Lucas M. BARBOSA (Fortaleza, Brazil)
Universidade Federal do Ceara, Campus do Pici, Bloco 914, Fortaleza,
Brazil
E-mail: [email protected]
Michael BILDHAUER (Saarlandes, Germany)
Universitiit des Saarlandes, D-66041 Saarbriicken, Germany
E-mail: [email protected]
Bernard DACOROGNA (Lausanne, Switzerland)
Ecole Poly technique Federale; 1015 Lausanne, Switzerland
E-mail: [email protected]
Robert FINN (Stanford, USA)
Stanford University, Stanford, CA 94305-2125, USA
E-mail: [email protected]
Martin FUCHS (Saarlandes, Germany)
Universitiit des Saarlandes, D-66041 Saarbriicken, Germany
E-mail: [email protected]
Yoshiko FUJIGAKI (Kobe, Japan)
Kobe University, Rokko, Kobe 657-8501, Japan
E-mail: [email protected]
Giovanni P. GALDI (Pittsburgh, USA)
University of Pittsburgh, 630 Benedum Hall, Pittsburgh, PA 15261, USA
E-mail: [email protected]
Stefan HILDEBRANDT (Bonn, Germany)
Mathematisches Institut der Universitiit Bonn, BeringstraBe 1, D-53115
Bonn, Germany
E-mail: [email protected]
xiii
