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Initial-Boundary Problems and the Navier-Stokes Equation

Initial-Boundary Problems and the Navier-Stokes Equation

Part of Classics in Applied Mathematics

  • 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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  • 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
    • 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

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