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The Three-Dimensional Navier–Stokes Equations
Classical Theory


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: September 2016
  • availability: Available
  • format: Hardback
  • isbn: 9781107019669
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About the Authors
  • A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.

    • Covers three cornerstone 'classical results' in the theory of the Navier–Stokes equations
    • Provides a thorough grounding of all the essential results in one convenient location
    • A self-contained source, accessible to graduates, which can be used for a course of one or two semesters
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    Reviews & endorsements

    'I loved this very well-written book and I highly recommend it.' Jean C. Cortissoz, Mathematical Reviews

    Customer reviews

    31st Jul 2017 by Xlwang

    This book is very comprehensive and easy to understand with respect to Navier-Stokes equation.

    Review was not posted due to profanity


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    Product details

    • Date Published: September 2016
    • format: Hardback
    • isbn: 9781107019669
    • length: 484 pages
    • dimensions: 235 x 157 x 31 mm
    • weight: 0.82kg
    • contains: 25 b/w illus. 115 exercises
    • availability: Available
  • Table of Contents

    Part I. Weak and Strong Solutions:
    1. Function spaces
    2. The Helmholtz–Weyl decomposition
    3. Weak formulation
    4. Existence of weak solutions
    5. The pressure
    6. Existence of strong solutions
    7. Regularity of strong solutions
    8. Epochs of regularity and Serrin's condition
    9. Robustness of regularity
    10. Local existence and uniqueness in H1/2
    11. Local existence and uniqueness in L3
    Part II. Local and Partial Regularity:
    12. Vorticity
    13. The Serrin condition for local regularity
    14. The local energy inequality
    15. Partial regularity I – dimB(S) ≤ 5/3
    16. Partial regularity II – dimH(S) ≤ 1
    17. Lagrangian trajectories
    A. Functional analysis: miscellaneous results
    B. Calderón–Zygmund Theory
    C. Elliptic equations
    D. Estimates for the heat equation
    E. A measurable-selection theorem
    Solutions to exercises

  • Authors

    James C. Robinson, University of Warwick
    James C. Robinson is a Professor of Mathematics at the University of Warwick.

    José L. Rodrigo, University of Warwick
    José L. Rodrigo is a Professor of Mathematics at the University of Warwick.

    Witold Sadowski, Uniwersytet Warszawski, Poland
    Witold Sadowski is an Assistant Professor in the Institute of Applied Mathematics at the University of Warsaw.

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