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Lecture Notes in Mathematical Fluid Mechanics

The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness

Authors: Ożański, Wojciech S.

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  • Provides a simple proof of the classical Caffarelli-Kohn-Nirenberg theorem with brevity and completeness
  • Promotes understanding of Scheffer’s constructions by providing streamlined proofs based on his arguments
  • Explains the geometric building blocks of the constructions by presenting numerous helpful figures
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eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-030-26661-5
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Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-030-26660-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-030-26661-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-030-26660-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness
Authors
Series Title
Lecture Notes in Mathematical Fluid Mechanics
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-26661-5
DOI
10.1007/978-3-030-26661-5
Softcover ISBN
978-3-030-26660-8
Series ISSN
2510-1374
Edition Number
1
Number of Pages
VI, 138
Number of Illustrations
23 b/w illustrations, 1 illustrations in colour
Topics