The Three-Dimensional Navier-Stokes Equations

Erscheinungsjahr 2016
ISBN: 978-1-107-01966-9
Verlag: Cambridge University Press

Buch, Englisch, Band 157, 484 Seiten, HC gerader Rücken kaschiert, Format (B × H): 157 mm x 235 mm, Gewicht: 935 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Robinson, James C.

Rodrigo, José L.

Sadowski, Witold

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

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

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

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