The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness
Springer International Publishing
ISBN 978-3-030-26661-5
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Bibliografische Daten
eBook. PDF
2019
VI, 138 p. 24 illus., 1 illus. in color..
In englischer Sprache
Umfang: 138 S.
Verlag: Springer International Publishing
ISBN: 978-3-030-26661-5
Weiterführende bibliografische Daten
Das Werk ist Teil der Reihe: Lecture Notes in Mathematical Fluid Mechanics Advances in Mathematical Fluid Mechanics
Produktbeschreibung
This 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.
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