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- W2804709625 abstract "Two main results will be presented in our paper. First, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a $log$ supercritical assumption on the horizontally radial component $u^r$ and vertical component $u^z$, accompanied by a $log$ subcritical assumption on the horizontally angular component $u^theta$ of the velocity. Second, the precise Green function for the operator $-(Delta-frac{1}{r^2})$ under the axially symmetric situation, where $r$ is the distance to the symmetric axis, and some weighted $L^p$ estimates of it will be given. This will serve as a tool for the study of axially symmetric Navier-Stokes equations. As an application, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a critical (or a subcritical) assumption on the angular component $w^theta$ of the vorticity." @default.
- W2804709625 created "2018-06-01" @default.
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- W2804709625 date "2018-05-27" @default.
- W2804709625 modified "2023-10-17" @default.
- W2804709625 title "Some Remarks on Regularity Criteria of Axially Symmetric Navier-Stokes Equations" @default.
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- W2804709625 doi "https://doi.org/10.48550/arxiv.1805.10752" @default.
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