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arXiv · 1806.07145

On some regularity criteria for axisymmetric Navier-Stokes equations

Joanna Rencławowicz·Wojciech M. Zajączkowski
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Abstract

We point out some criteria that imply regularity of axisymmetric solutions to Navier-Stokes equations. We show that boundedness of $\|{v_{r}}/{\sqrt{r^3}}\|_{L_2({\rm R}^3\times (0,T))}$ as well as boundedness of $\|{\omega_{\varphi}}/{\sqrt{r}}\|_{L_2({\rm R}^3\times (0,T))},$ where $v_r$ is the radial component of velocity and $\omega_{\varphi}$ is the angular component of vorticity, imply regularity of weak solutions.

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Joanna Rencławowicz, Wojciech M. Zajączkowski. 2018-06-19. On some regularity criteria for axisymmetric Navier-Stokes equations. https://doi.org/10.1007/s00021-019-0447-0

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