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Author:   Pierre-Louis Lions (Professor of Mathematics, University of Paris-Dauphine, and of Applied Mathematics, Ecole Polytechnique)
Publisher:   Oxford University Press
Imprint:   Clarendon Press
Volume:   3
Dimensions:   Width: 16.20cm , Height: 1.90cm , Length: 24.10cm
Weight:   0.517kg
ISBN:  

9780198514879

ISBN 10:   0198514875
Pages:   252
Publication Date:   27 June 1996
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Preface ; Table of contents ; 1. Presentation of the models ; Part 1: Incompressible Models ; 2. Density-dependent Navier-Stokes equations ; 3. Navier-Stokes equations ; 4. Euler equations and other incompressible models ; Appendix A Truncation of divergence-free vectorfields ; Appendix B Two facts on D1,2(R2) ; Appendix C Compactness in time with values in weak topologies ; Appendix D Weak L1 estimates for solutions of the heat equation ; Appendix E A short proof of the existence of renormalized solutions for parabolic equations ; Intended Table of Contents of Volume 2 ; Part 2: Compressible Models ; 5. Compactness results for compressible isentropic Navier-Stokes ; 6. Stationary problems ; 7. Existence results ; 8. Related questions ; Part 3: Asymptotic limites ; 9. Asymptotic limits

Reviews

A lot of results are new, and for each of these recent results the complete and self-contained proofs are given...Summarizing the impression of this interesting book, it is worth pointing out that it is written in an easy-reading fashion along with the deep and comprehensive analysis of the topics which are at the highest level of the importance in the modern theory of nonlinear differential equations Zentralblatt fur Mathematik 866-487 Everybody who is interested in studying mathematical questions arisng in fluid mechanics should read this book. (joma) ...the material presented in the book is not only essential in the mathematical treatment of fluid mechanics but also in many other fields where the theory of non linear partial differential equations plays an important role. Its reading will become a must for researchers in this area of mathematics. European Journal of Mechanics, B/Fluids, vol. 17, no. 3, May - June 1998 The book in question goes far beyond the scope of the existing monographs on Euler and Navier Stokes equations, reaches the current frontiers of research, and points to numerous extensions or open problems... The text...is written in a clear and precise, but nevertheless lively style. SIAM Review, vol. 40, no. 2, June 1998 Without doubt the monograph will soon become one of the main references on the mathematical analysis of fluid mechanics and should be on the bookshelves of every researcher in the field. Having read the first volume I am looking forward to the second volume on compressible volumes. SIAM Review, vol. 40, no. 2, June 1998 the gathering of rigorous results in an easily accessible publication with an extensive bibliography will be of benefit to all workers in theoretical Fluid mechanics. Mathematika, 44 Everybody who is interested in studying mathematical questions arising in fluid mechanics should read this book. European Mathematical Society, issue 27, March 1998

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