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Initial-Boundary Problems and the Navier-Stokes Equation

Part of Classics in Applied Mathematics

Authors:
Heinz-Otto Kreiss, University of California, Los Angeles
Jens Lorenz, University of New Mexico

Date Published: January 2004
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Paperback
isbn: 9780898715651

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Description

This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. 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 reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
- Continues to be useful to researchers and graduate students in applied mathematics and engineering
- Functional analytical prerequisites were kept to a minimum or were developed in the book, making it accessible to a wide audience
- The direct approach to the subject still gives a valuable introduction to an important area of applied analysis
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Product details
- Date Published: January 2004
- format: Paperback
- isbn: 9780898715651
- length: 420 pages
- dimensions: 258 x 154 x 20 mm
- weight: 0.57kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface to the Classics Edition
Introduction
1. The Navier-Stokes equations
2. Constant-coefficient Cauchy problems
3. Linear variable-coefficient Cauchy problems in 1D
4. A nonlinear example: Burgers' equations
5. Nonlinear systems in one space dimension
6. The Cauchy problem for systems in several dimensions
7. Initial-boundary value problems in one space dimension
8. Initial-boundary value problems in several space dimensions
9. The incompressible Navier-Stokes equations: the spatially periodic case
10. The incompressible Navier-Stokes equations under initial and boundary conditions
Appendices
References
Author index
Subject index.
Authors
Heinz-Otto Kreiss, University of California, Los Angeles
Jens Lorenz, University of New Mexico