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OverviewThis monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer’s constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable. Full Product DetailsAuthor: Wojciech S. OżańskiPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2019 Weight: 0.454kg ISBN: 9783030266608ISBN 10: 3030266605 Pages: 138 Publication Date: 17 September 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 Introduction.- 2 The Caffarelli-Kohn-Nirenberg theorem.- 3 Point blow-up.- 4. Blow-up on a Cantor set.ReviewsThis is a well written, and this makes it easy to read, mathematical text. ... Essentially self-contained, the book can be used as a straightforward introduction to the topic of regularity of solutions of the Navier-Stokes equations. (Florin Catrina, zbMATH 1441.35004, 2020) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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