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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness/ by Wojciech S. Ożański.
Author:	Ożański, Wojciech S.
Description:	VI, 138 p. 24 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential 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
Ożański, Wojciech S.

The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness[electronic resource] /by Wojciech S. Ożański. - 1st ed. 2019. - VI, 138 p. 24 illus., 1 illus. in color.online resource. - Lecture Notes in Mathematical Fluid Mechanics,2510-1374. - Lecture Notes 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:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

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