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Initial-Boundary Value Problems and the Navier-Stokes Equations

Heinz-Otto Kreiss and Jens Lorenz
Publisher: 
SIAM
Publication Date: 
2004
Number of Pages: 
402
Format: 
Paperback
Series: 
Classics In Applied Mathematics 47
Price: 
48.00
ISBN: 
0-89871-565-2
Category: 
Monograph
[Reviewed by
Fernando Q. Gouvêa
, on
12/1/2004
]
A Telegraphic Review in the October 1989 issue of the Monthly described this book as follows: "Develops a theory for linear and nonlinear equations for problems well-suited to computation, examining smoothness and admissible boundary conditions in great detail. Illustrates the theory with careful study of compressible and incompressible Navier-Stokes equations." This edition, in SIAM's Classics in Mathematics series, is an unaltered reprint of the original 1989 book.

A longer review appeared in SIAM Review, December 1990. It can be accessed through JSTOR.

Preface to the Classics Edition; Errata; Introduction; Chapter 1: The Navier-Stokes Equations; Chapter 2: Constant-Coefficient Cauchy Problems; Chapter 3: Linear Variable-Coefficient Cauchy Problems in 1D; Chapter 4: A Nonlinear Example: Burgers' Equations; Chapter 5: Nonlinear Systems in One Space Dimension; Chapter 6: The Cauchy Problem for Systems in Several Dimensions; Chapter 7: Initial-Boundary Value Problems in One Space Dimension; Chapter 8: Initial-Boundary Value Problems in Several Space Dimensions; Chapter 9: The Incompressible Navier-Stokes Equations: The Spatially Periodic Case; Chapter 10: The Incompressible Navier-Stokes Equations under Initial and Boundary Conditions; Appendix 1: Notations and Results from Linear Algebra; Appendix 2: Interpolation; Appendix 3: Sobolev Inequalities; Appendix 4: Application of the Arzela-Ascoil Theorem; References; Author Index; Subject Index.

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