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

2022/01/05 by Chen, Hui, Tsai, Tai-Peng, Zhang, Ting
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.01766

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,x₃,t)|≤ N e^-c |ln r|^τ, 0

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