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Erschienen in:
Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

16. Regularity Criteria for Navier-Stokes Solutions

verfasst von : Gregory Seregin, Vladimir Šverák

Erschienen in: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Verlag: Springer International Publishing

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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.

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Vorheriges Kapitel The Inviscid Limit and Boundary Layers for Navier-Stokes Flows
Nächstes Kapitel Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations
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Metadaten
Titel
Regularity Criteria for Navier-Stokes Solutions
verfasst von
Gregory Seregin
Vladimir Šverák
Copyright-Jahr
2018
Buch
Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Print ISBN: 978-3-319-13343-0

Electronic ISBN: 978-3-319-13344-7

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-13344-7_16