Local regularity of axisymmetric solutions to the Navier–Stokes equations

In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier–Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier–Stokes equations have no Type I blowups.

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Bibliographic Details
Published in:Analysis and mathematical physics 2020-12, Vol.10 (4), Article 46
Main Author: Seregin, G.
Format: Article
Language:English
Subjects:
Analysis
Fluid dynamics
Fluid flow
Harmonic Analysis and PDE dedicated to Vladimir Maz’ya
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Regularity
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Description
Summary:In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier–Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier–Stokes equations have no Type I blowups.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-020-00392-1