The Three-Dimensional Navier-Stokes Equations

Classical Theory

AvJames C. Robinson,José L. Rodrigo

Inbunden, Engelska, 2016

Del 157 i serien Cambridge Studies in Advanced Mathematics

942 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-09-07
Mått:157 x 235 x 31 mm
Vikt:820 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:484
Förlag:Cambridge University Press
ISBN:9781107019669

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

James C. Robinson is a Professor of Mathematics at the University of Warwick. José L. Rodrigo is a Professor of Mathematics at the University of Warwick. Witold Sadowski is an Assistant Professor in the Institute of Applied Mathematics at the University of Warsaw.

Recensioner i media

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

Innehållsförteckning

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.