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

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 present...

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Autor principal: Ożański, Wojciech S
Lenguaje:eng
Publicado: Springer 2019
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-030-26661-5
http://cds.cern.ch/record/2691312
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author Ożański, Wojciech S
author_facet Ożański, Wojciech S
author_sort Ożański, Wojciech S
collection CERN
description 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.
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spelling cern-26913122021-04-21T18:19:32Zdoi:10.1007/978-3-030-26661-5http://cds.cern.ch/record/2691312engOżański, Wojciech SThe partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpnessMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:26913122019
spellingShingle Mathematical Physics and Mathematics
Ożański, Wojciech S
The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
title The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
title_full The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
title_fullStr The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
title_full_unstemmed The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
title_short The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness
title_sort partial regularity theory of caffarelli, kohn, and nirenberg and its sharpness
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-030-26661-5
http://cds.cern.ch/record/2691312
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