Initial-boundary value problems and the Navier-Stokes equations [electronic resource] / Heinz-Otto Kreiss, Jens Lorenz.

Kreiss, H. (Heinz-Otto)
Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2004.
Classics in applied mathematics ; 47.
Classics in applied mathematics ; 47
Classics in applied mathematics ; 47
1 electronic text (xvii, 402 p.) : ill., digital file.
Initial value problems.
Boundary value problems.
Navier-Stokes equations.
System Details:
Mode of access: Internet via World Wide Web.
Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.
The Navier-Stokes equations
Constant-coefficient Cauchy problems
Linear variable-coefficient Cauchy problems in 1D
A nonlinear example: Burgers' equations
Nonlinear systems in one space dimension
The Cauchy problem for systems in several dimensions
Initial-boundary value problems in one space dimension
Initial-boundary value problems in several space dimensions
The incompressible Navier-Stokes equations: the spatially periodic case
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.
Digitized and made available by:
Originally published: Boston : Academic Press, c1989.
Includes bibliographical references (p. 393-398) and index.
Description based on title page of print version.
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Lorenz, Jens, 1949-
Publisher Number:
CL47 siam
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Restricted to subscribers or individual electronic text purchasers.
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