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Local regularity of axisymmetric solutions to the Navier–Stokes equations

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Abstract

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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Acknowledgements

The work is supported by the Grant RFBR 20-01-00397.

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Authors and Affiliations

  1. OxPDE, Mathematical Institute, University of Oxford, Oxford, UK

    G. Seregin

  2. St Petersburg Department of V A Steklov Mathematical Institute, Saint Petersburg, Russia

    G. Seregin

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  1. G. Seregin
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Correspondence to G. Seregin.

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Dedicated to Vladimir Gilelevich Mazya.

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Seregin, G. Local regularity of axisymmetric solutions to the Navier–Stokes equations. Anal.Math.Phys. 10, 46 (2020). https://doi.org/10.1007/s13324-020-00392-1

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  • DOI: https://doi.org/10.1007/s13324-020-00392-1

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