Instability in Models Connected with Fluid Flows II

Instability in Models Connected with Fluid Flows II presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations,

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INTERNATIONAL MATHEMATICAL SERIES Series Editor: Tamara Rozhkovskaya Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

1. Nonlinear Problems in Mathematical Physics and Related Topics I. In Honor of Professor O.A. Ladyzhenskaya • M.Sh. Birman, S. Hildebrandt, V.A. Solonnikov, N.N. Uraltseva Eds. • 2002 2. Nonlinear Problems in Mathematical Physics and Related Topics II. In Honor of Professor O.A. Ladyzhenskaya • M.Sh. Birman, S. Hildebrandt, V.A. Solonnikov, N.N. Uraltseva Eds. • 2003 3. Different Faces of Geometry • S. Donaldson, Ya. Eliashberg, M. Gromov Eds. • 2004 4. Mathematical Problems from Applied Logic I. Logics for the XXIst Century • D. Gabbay, S. Goncharov, M. Zakharyaschev Eds. • 2006 5. Mathematical Problems from Applied Logic II. Logics for the XXIst Century • D. Gabbay, S. Goncharov, M. Zakharyaschev Eds. • 2007 6. Instability in Models Connected with Fluid Flows I • C. Bardos, A. Fursikov Eds. • 2008 7. Instability in Models Connected with Fluid Flows II • C. Bardos, A. Fursikov Eds. • 2008

Instability in Models Connected with Fluid Flows II Edited by

Claude Bardos Université Denis Diderot Laboratoire J.-L. Lions, Université 6 Paris, France

Andrei Fursikov Moscow State University Institute of Numerical Mathematics RAS Moscow, Russia

Editors Claude Bardos Université Denis Diderot Laboratoire J.-L. Lions, Université 6 Paris, France

Andrei Fursikov Moscow State University Institute of Numerical Mathematics RAS Moscow, Russia

This series was founded by Kluwer / Plenum Publishers (now Springer) and the Russian publisher Tamara Rozhkovskaya (Novosibirsk, Russia, [email protected]) in 2002. Each volume presents contributions from volume editors and authors invited by the Series Editor. The English Camera-Ready Manuscript was prepared by Tamara Rozhkovskaya.

Library of Congress Control Number: 2007938320 ISBN: 978-0-387-75218-1 ISSN: 1571-5485

e-ISBN: 978-0-387-75219-8

c 2008 Springer Science+Business Media, LLC  All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper. 9 8 7 6 5 4 3 2 1 springer.com

Instability in Models Connected with Fluid Flows I, II

Two volumes of the International Mathematical Series present various topics on control theory, free boundary problems, the Navier–Stokes equations, attractors, first order linear and nonlinea