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

• Main Author: Ożański, Wojciech S. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Lecture Notes in Mathematical Fluid Mechanics,
• Subjects: Partial differential equations.; Mathematical physics.; Fluids.; Partial Differential Equations.; Mathematical Applications in the Physical Sciences.; Fluid- and Aerodynamics.

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...

Table of Contents:

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