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arXiv · 2201.01766

Remarks on local regularity of axisymmetric solutions to the 3D Navier--Stokes equations

Hui Chen·Tai-Peng Tsai·Ting Zhang
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Abstract

In this note, a new local regularity criteria for the axisymmetric solutions to the 3D Navier--Stokes equations is investigated. It is slightly supercritical and implies an upper bound for the oscillation of $Γ=r u^θ$: for any $0< τ<1$, there exists a constant $c>0$, $$ |Γ(r,x_{3},t)|\leq N e^{-c\, |\ln r|^τ},\ 0<r\leq \frac{1}{4}. $$

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Hui Chen, Tai-Peng Tsai, Ting Zhang. 2022-01-05. Remarks on local regularity of axisymmetric solutions to the 3D Navier--Stokes equations. https://arxiv.org/abs/2201.01766

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