Mathematical Topics in Fluid Mechanics: Volume 1: Incompressible Models (Mathematical Topics in Fluid Mechanics Vol. 3) [Hardcover]

Pierre-Louis Lions (Author)

Book Description

ISBN-10: 0198514875 | ISBN-13: 978-0198514879 | Publication Date: August 29, 1996

One of the most challenging topics in applied mathematics is the development of the theory of nonlinear partial different equations. Many problems in mechanics, geometry, and probability lead to such equations when formulated in mathematical terms. Yet despite a long history of contributions, no core theory has been formulated. Written by the winner of the 1994 Fields Medal, this outstanding two-volume work helps shed new light on this important topic. Volume 1 emphasizes the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, a profound and self-contained study of both the classical Navier-Stokes equations (including the inhomogeneous case) and the Euler equations is given. Results about the existence and regularity of solutions are presented with complete proofs. The text highlights in particular the use of modern analytical tools and methods, and it indicates many open problems. Mathematical Topics in Fluid Mechanics will be an indispensable reference for every researcher in the field. Its topicality and the clear, concise presentations by the author make it an outstanding contribution to the great theoretical problems concerning mathematical modelling of physical phenomena.

Editorial Reviews

Review

`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

About the Author

Pierre-Louis Lions is a Professor of Mathematics, University of Paris-Dauphine, and of Applied Mathematics at Ecole Polytechnique.

Product Details

• Hardcover: 256 pages
• Publisher: Oxford University Press, USA (August 29, 1996)
• Language: English
• ISBN-10: 0198514875
• ISBN-13: 978-0198514879
• Product Dimensions: 9.6 x 6 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #2,796,308 in Books (See Top 100 in Books)