The three-dimensional Navier-Stokes equations : classical theory /
James C. Robinson, José L. Rodrigo, Witold Sadowski.
- 1 online resource (xiv, 471 pages) : digital, PDF file(s).
- Cambridge studies in advanced mathematics ; 157 .
- Cambridge studies in advanced mathematics ; 157. .
Title from publisher's bibliographic system (viewed on 07 Sep 2016).
A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier-Stokes equations, this book provides self-contained proofs of someof the most significant results in the area, many of which can only be found in researchpapers. Highlights include the existence of global-in-time Leray-Hopf weak solutionsand the local existence of strong solutions; the conditional local regularity results ofSerrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg.Appendices provide background material and proofs of some 'standard results' thatare hard to find in the literature. A substantial number of exercises are included, with fullsolutions given at the end of the book. As the only introductory text on the topic to treatall of the mainstream results in detail, this book is an ideal text for a graduate course ofone or two semesters. It is also a useful resource for anyone working in mathematicalfluid dynamics.