Regularity criteria for navier-stokes solutions

Gregory Seregin, Vladimir Sverak

Research output: Chapter in Book/Report/Conference proceedingChapter

9 Scopus citations

Abstract

In this chapter some of the known regularity criteria for the weak solution of the incompressible 3D Navier-Stokes equations are discussed. At present the problem of regularity of general solutions starting from smooth data is open, and all the criteria involve an assumption on a suitable quantity which is invariant under the scaling symmetry of the equations. Both interior regularity and boundary regularity are addressed. The methods developed by Scheffer and Caffarelli-Kohn-Nirenberg play an important role. Simple but important considerations based on dimensional analysis and the scaling symmetry are recalled, together with some heuristics. Connections between the Liouville-type theorems and Type I singularities are also discussed. Proofs of some statements which are not easily accessible in the literature are presented.

Original languageEnglish (US)
Title of host publicationHandbook of Mathematical Analysis in Mechanics of Viscous Fluids
PublisherSpringer International Publishing
Pages829-867
Number of pages39
ISBN (Electronic)9783319133447
ISBN (Print)9783319133430
DOIs
StatePublished - Apr 19 2018

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