國立高雄大學圖資館 |

Language: English

Back

The partial regularity theory of Caf...

Ozanski, Wojciech S.

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 sharpnessby Wojciech S. Ozanski.
Author:	Ozanski, Wojciech S.
Published:	Cham :Springer International Publishing :2019.
Description:	vi, 138 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Navier-Stokes equations.
Online resource:	https://doi.org/10.1007/978-3-030-26661-5
ISBN:	9783030266615$q(electronic bk.)

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$q(electronic bk.)

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

229271
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
LDR:02015nmm a2200337 a 4500 001 566483
003 DE-He213
005 20191223142109.0
006 m d
007 cr nn 008maaau
008 200429s2019 gw s 0 eng d
020 $a 9783030266615$q(electronic bk.)
020 $a 9783030266608$q(paper)
024 7 $a 10.1007/978-3-030-26661-5 $2 doi
035 $a 978-3-030-26661-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA374 $b .O368 2019
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 518.64 $2 23
090 $a QA374 $b .O99 2019
100 1 $a Ozanski, Wojciech S. $3 852200
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 229271
650 1 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 522718
650 2 4 $a Fluid- and Aerodynamics. $3 376797
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Advances in mathematical fluid mechanics. $3 677395
856 4 0 $u https://doi.org/10.1007/978-3-030-26661-5
950 $a Mathematics and Statistics (Springer-11649)