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

Wojciech S. Ożański (Autor)

Buch | Softcover

VI, 138 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-26660-8 (ISBN)

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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.

1 Introduction.- 2 The Caffarelli-Kohn-Nirenberg theorem.- 3 Point blow-up.- 4. Blow-up on a Cantor set.

"This 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)

Erscheinungsdatum	18.09.2019
Reihe/Serie	Advances in Mathematical Fluid Mechanics
Reihe/Serie	Lecture Notes in Mathematical Fluid Mechanics
Zusatzinfo	VI, 138 p. 24 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	231 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
Schlagworte	Cafarelli-Kohn-Nirenberg partial regularity theore • Cafarelli-Kohn-Nirenberg partial regularity theorem • Caffarelli-Kohn-Nirenberg • Caffarelli-Kohn-Nirenberg book • Caffarelli-Kohn-Nirenberg inequalities • Caffarelli-Kohn-Nirenberg theorem simple • fluid- and aerodynamics • Leray-Hopf weak solutions • Local energy inequality • navier-stokes equations • Partial differential equations • Partial regularity theory • Scheffer constructions • Vladimir Scheffer • Weak solutions to the Navier-Stokes inequality
ISBN-10	3-030-26660-5 / 3030266605
ISBN-13	978-3-030-26660-8 / 9783030266608
Zustand	Neuware