The three-dimensional Navier-Stokes equations: classical theory
by Robinson, James C., (James Cooper)
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 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,…
Read More ↓Title Statements
- Full title :The three-dimensional Navier-Stokes equations : classical theory / James C. Robinson, University of Warwick ; José L. Rodrigo, University of Warwick ; Witold Sadowski, University of Warsaw.
Summary
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 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 mathematical fluid dynamics.
Read More ↓Edition Statements
- Publication Date:©2016
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:©2016
Notes
Title from publisher's bibliographic system (viewed on 07 Sep 2016).
The Physical Object
- Description:1 online resource (xiv, 471 pages) : : illustrations
Edition Identifiers
- ISBN:9781139095143, 1139095145
- oclc:ocn959692448
- LC Classification:QA374
- Dewey Decimal:515/.353
Table of Contents
Function spaces -- The Helmholtz-Weyl decomposition -- Weak formulation -- Existence of weak solutions -- The pressure -- Existence of strong solutions -- Regularity of strong solutions -- Epochs of regularity and Serrin's condition -- Robustness of regularity and convergence of Galerkin approximations -- Local existence and uniqueness in H1/2 -- Local existence and uniqueness in L3 -- Vorticity -- The Serrin condition for local regularity -- The local energy inequality -- Partial regularity I -- Partial regularity II -- Langrangian trajectories.
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