The Three-Dimensional Navier–Stokes Equations
The Three-Dimensional Navier–Stokes Equations
José L. Rodrigo, University of Warwick
Witold Sadowski, Uniwersytet Warszawski, Poland
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
Reviews & endorsements
'I loved this very well-written book and I highly recommend it.' Jean C. Cortissoz, Mathematical Reviews
Product details
No date availableHardback
9781107019669
484 pages
235 × 157 × 31 mm
0.82kg
25 b/w illus. 115 exercises
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
- References
- Index.
