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Seregin, G.

Local regularity of axisymmetric solutions to the Navier-Stokes equations. (English) Zbl 1527.35217

Golberg, Anatoly (ed.) et al., Harmonic analysis and partial differential equations. In honor of Vladimir Maz’ya. Selected papers based on the presentations at the international conference, Holon, Israel, May 26–31, 2019. Cham: Birkhäuser. 275-294 (2023).
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.
For the entire collection see [Zbl 1515.42003].

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35B44 Blow-up in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35B07 Axially symmetric solutions to PDEs

Keywords:

Navier-Stokes equations; axisymmetric solutions; local regularity
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References:

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