The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness
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
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Wojciech S. Oz˙an´ski
The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness
Advances in Mathematical Fluid Mechanics Lecture Notes in Mathematical Fluid Mechanics
Editor-in-Chief Giovanni P Galdi University of Pittsburgh, Pittsburgh, PA, USA
Series Editors Didier Bresch Université Savoie-Mont Blanc, Le Bourget du Lac, France Volker John Weierstrass Institute, Berlin, Germany Matthias Hieber Technische Universität Darmstadt, Darmstadt, Germany Igor Kukavica University of Southern California, Los Angles, CA, USA James Robinson University of Warwick, Coventry, UK Yoshihiro Shibata Waseda University, Tokyo, Japan
Lecture Notes in Mathematical Fluid Mechanics as a subseries of “Advances in Mathematical Fluid Mechanics” is a forum for the publication of high quality monothematic work as well lectures on a new field or presentations of a new angle on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations and other significant viscous and inviscid fluid models. In particular, mathematical aspects of computational methods and of applications to science and engineering are welcome as an important part of the theory as well as works in related areas of mathematics that have a direct bearing on fluid mechanics.
More information about this subseries at http://www.springer.com/series/15480
Wojciech S. Ożański
The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness
Wojciech S. Ożański Department of Mathematics University of Southern California Los Angeles, CA, USA
ISSN 2297-0320 ISSN 2297-0339 (electronic) Advances in Mathematical Fluid Mechanics ISSN 2510-1374 ISSN 2510-1382 (electronic) Lecture Notes in Mathematical Fluid Mechanics ISBN 978-3-030-26660-8 ISBN 978-3-030-26661-5 (eBook) https://doi.org/10.1007/978-3-030-26661-5 Mathematics Subject Classification (2010): 35Q30, 76D05, 76D03 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publish
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