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Navier-Stokes Equations and Nonlinear Functional Analysis

Navier-Stokes Equations and Nonlinear Functional Analysis

2nd Edition

Part of CBMS-NSF Regional Conference Series in Applied Mathematics

  • Author: Roger Temam, Université de Paris-Sud, Orsay, France
  • Date Published: December 1996
  • availability: Available in limited markets only
  • format: Paperback
  • isbn: 9780898713404

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  • This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds.

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    Product details

    • Edition: 2nd Edition
    • Date Published: December 1996
    • format: Paperback
    • isbn: 9780898713404
    • length: 155 pages
    • dimensions: 252 x 173 x 10 mm
    • weight: 0.278kg
    • availability: Available in limited markets only
  • Table of Contents

    Preface to the second edition
    Introduction
    Part I. Questions Related to the Existence, Uniqueness and Regularity of Solutions:
    1. Representation of a Flow: the Navier-Stokes Equations
    2. Functional Setting of the Equations
    3. Existence and Uniqueness Theorems (Mostly Classical Results)
    4. New a priori Estimates and Applications
    5. Regularity and Fractional Dimension
    6. Successive Regularity and Compatibility Conditions at t=0 (Bounded Case)
    7. Analyticity in Time
    8. Lagrangian Representation of the Flow
    Part II. Questions Related to Stationary Solutions and Functional Invariant Sets (Attractors):
    9. The Couette-Taylor Experiment
    10. Stationary Solutions of the Navier-Stokes Equations
    11. The Squeezing Property
    12. Hausdorff Dimension of an Attractor
    Part III. Questions Related to the Numerical Approximation:
    13. Finite Time Approximation
    14. Long Time Approximation of the Navier-Stokes Equations
    Appendix. Inertial Manifolds and Navier-Stokes Equations
    Comments and Bibliography
    Comments and Bibliography
    Update for the Second Edition
    References.

  • Author

    Roger Temam, Université de Paris-Sud, Orsay, France

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