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

1. Auflage 2019
ISBN: 978-3-030-26660-8
Verlag: Springer International Publishing

Buch, Englisch, 138 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 230 g

Reihe: Lecture Notes in Mathematical Fluid Mechanics

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.

Zielgruppe

Research

Autoren/Hrsg.

O¿a¿ski, Wojciech S.

Ozanski, Wojciech S.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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