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The partial regularity theory of Caf...

Ozanski, Wojciech S.

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The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness

Record Type:	Electronic resources : Monograph/item
Title/Author:	The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness/ by Wojciech S. Ozanski.
Author:	Ozanski, Wojciech S.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	vi, 138 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Introduction -- 2 The Caffarelli-Kohn-Nirenberg theorem -- 3 Point blow-up -- 4. Blow-up on a Cantor set.
Contained By:	Springer eBooks
Subject:	Navier-Stokes equations. -
Online resource:	https://doi.org/10.1007/978-3-030-26661-5
ISBN:	9783030266615

The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
Ozanski, Wojciech S.

The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness[electronic resource] /by Wojciech S. Ozanski. - Cham :Springer International Publishing :2019. - vi, 138 p. :ill., digital ;24 cm. - Advances in mathematical fluid mechanics. - Advances in mathematical fluid mechanics..

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

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.

ISBN: 9783030266615

Standard No.: 10.1007/978-3-030-26661-5doiSubjects--Topical Terms:

628091
Navier-Stokes equations.

LC Class. No.: QA374 / .O368 2019

Dewey Class. No.: 518.64

The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
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100 1 $a Ozanski, Wojciech S. $3 3414448
245 1 4 $a The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness $h [electronic resource] / $c by Wojciech S. Ozanski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a vi, 138 p. : $b ill., digital ; $c 24 cm.
490 1 $a Advances in mathematical fluid mechanics
505 0 $a 1 Introduction -- 2 The Caffarelli-Kohn-Nirenberg theorem -- 3 Point blow-up -- 4. Blow-up on a Cantor set.
520 $a 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.
650 0 $a Navier-Stokes equations. $3 628091
650 1 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
650 2 4 $a Fluid- and Aerodynamics. $3 1066670
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830 0 $a Advances in mathematical fluid mechanics. $3 2057138
856 4 0 $u https://doi.org/10.1007/978-3-030-26661-5
950 $a Mathematics and Statistics (Springer-11649)